high accuracy numerical methods for the gardner ostrovsky equation the gardner ostrovsky equation also known as the extended rotation modified korteweg de vries kdv equation describes weakly nonlinear internal oceanic waves under the influence of earth rotation high accuracy numerical methods are needed to follow with precision the long time evolution of the solutions of this equation with the additional difficulty that the numerical methods have to conserve very accurately several invariants of the solutions including the mass and the energy of the waves finite difference methods traditionally used for the solution of the kdv equation fails to preserve accurately these invariants for large times in this paper we show that this difficulty can be overcome by using a high accuracy finite difference hafd numerical method we present a strong stability preserving finite difference scheme and compare its performance using some relevant examples with those of two recently published numerical methods for solving this kind of equation a simpler second order finite difference method and a pseudospectral numerical scheme that enforces the conservation of energy the numerical comparison shows that the three methods have similar accuracy for short times but the simpler finite difference scheme is less accurate in preserving the three invariants affecting the numerical accuracy of the solution as time goes on on the contrary the hafd method presented here preserves the invariants with even better accuracy than the pseudospectral scheme but with a much lower computational cost in addition the numerical implementation of the hafd method is as easy as that of the simpler finite difference method being both much simpler than the intricate energy conservation pseudospectral scheme these advantages makes the hafd method presented here very appropriate for solving numerically this type of equations particularly for studying long time wave propagation

effects of the lattice point drivers heterogeneity of the disturbance risk preference on traffic flow instability abstract this paper defines the lattice point drivers heterogeneity of the disturbance risk preference and proposes a new one dimensional traffic flow lattice model to research the effects of the lattice point drivers heterogeneity of the disturbance risk preference on traffic flow instability by the analytical analysis we obtain the traffic flow instability condition and the modified korteweg de vries mkdv equation and the calculation formula of the unstable area density range and the calculation method of the probability of traffic congestion caused by a small disturbance both the analytical and the simulation analysis show that there are important effects of the lattice point drivers heterogeneity of the disturbance risk preference on traffic flow instability namely the smaller the ratio of the preceding lattice point drivers coefficient of the disturbance risk preference to the following lattice point drivers coefficient of the disturbance risk preference is the smaller the traffic flow instability is and vice versa it provides a viable idea to ease traffic congestion

a rigid local system with monodromy group the big conway group 2 and two others with monodromy group the suzuki group 6

brauer characters and rationality a finite group g has no non trivial rational valued irreducible p brauer characters if and only if g has no non trivial rational elements of order not divisible by p

analytical and numerical studies of the variable coefficient gardner equation the gardner or extended korteweg de vries equation with the variable sign cubic non linear term is studied this equation occurred in the theory of interfacial waves in the stratified shear flow at some certain conditions on the medium stratification an asymptotic method is applied to study the solitary wave transformation when the coefficient of the cubic non linear term is varied slowly it is found the one branch of the solitary waves destroys in the vicinity of the bifurcation point where the exponential soliton transforms into the breather through algebraic soliton other solitary waves change their amplitude accordingly to the cubic non linear term variation the structure of the tail formed behind the solitary wave is determined direct numerical simulation of the gardner equation is performed to analyze the transformation and breaking of the solitary wave it confirms most of the theoretical results the calculated dynamics of the table top soliton due to the large values of the mass and momentum integrals differs from the asymptotic prediction because the characteristic time of the variation of the cubic non linear term has the same order as the duration of table top soliton

tdgl and mkdv equations for jamming transition in the lattice models of traffic abstract the lattice models of traffic are proposed to describe the jamming transition in traffic flow on a highway in terms of thermodynamic terminology of phase transitions and critical phenomena they are the lattice versions of the hydrodynamic model of traffic two lattice models are presented one is described by the differential difference equation where time is a continuous variable and space is a discrete variable and the other is the difference equation in which both time and space variables are discrete we apply the linear stability theory and the nonlinear analysis to the lattice models it is shown that the time dependent ginzburg landau tdgl equation is derived to describe the traffic flow near the critical point a thermodynamic theory is formulated for describing the phase transitions and critical phenomena it is also shown that the perturbed modified korteweg de vries mkdv equation is derived to describe the traffic jam

interaction of a solitary wave with an external force abstract using the forced korteweg de vries equation as a model we investigate the interaction of a solitary wave with an isolated moving external force of small amplitude we use both analysis and numerical calculations our analysis is based on a multi scale perturbation asymptotic analysis and is carried through to either the first or second order depending on whether the first or more accurate second order expression for the solitary wave speed is used the perturbation theory leads to a pair of autonomous equations for the solitary wave amplitude and position and these are analyzed in detail for the two extreme cases when the lengthscale of the external force is either much greater or much less than that of the solitary wave the theory predicts that the main regimes are passage when the solitary wave passes through the external force with some amplitude modulation repulsion when the solitary wave is reflected by the external force with a significant amplitude change and trapping when the solitary wave remains either partially or totally trapped at the location of the external force these theoretical predictions are confirmed in our numerical simulations of the forced korteweg de vries equation

a delayed feedback control method for the lattice hydrodynamic model caused by the historic density difference effect abstract a delayed feedback control pattern is brought forward for lattice hydrodynamic model of traffic flow with the consideration of the historic density difference effect we utilize the modern control theory to obtain the linear stability conditions with the consideration of feedback control signal which shows that the stability of traffic flow is closely related to the information of the historic density difference furthermore numerical simulations affirm that the delayed feedback control signal can suppress the traffic congestion efficiently

analysis of the response of a strongly nonlinear damped system using a differential transformation technique the differential transformation technique is applied to solve a nonlinear differential equation that describes the underdamped and the overdamped motion of a system subjected to external excitations numerical results are compared to those obtained by the runge kutta method to illustrate the preciseness and effectiveness of the proposed method

interactions of solitons in nonintegrable systems direct perturbation method and applications abstract problems of approximate description of soliton interaction in nonintegrable systems are discussed it is shown that in an arbitrary lagrangian system in the first nontrivial order of the small parameter asymptotic scheme for a system of solitons with close velocities a lagrangian may be introduced analogous to that for classical particles with a pair interaction potential a classification of possible types of soliton interaction is given and criteria of the existence of bound states are formulated a possibility of generalization of approximated description of soliton interaction in the multidimensional case is noted

an extended car following model considering driver s sensory memory and the backward looking effect abstract on the basis of full velocity difference model fvdm an extended car following model is proposed to account for the effect of driver s memory and backward looking effect in this paper the stability conditions of the new model are derived by applying the linear stability analysis the time dependent ginzburg lan tdgl equation and the modified korteweg de vries mkdv equation are derived through nonlinear theory moreover the relationship between the two equations is studied numerical simulations show that the stability of traffic flows can be strengthened with the effect of driver s memory and backward looking effect

local systems and finite unitary and symplectic groups abstract for powers q of any odd prime p and any integer n 2 we exhibit explicit local systems on the affine line a 1 in characteristic p 0 if 2 n and on the affine plane a 2 if 2 n whose geometric monodromy groups are the finite symplectic groups sp 2 n q when n 3 is odd we show that the explicit rigid local systems on the affine line in characteristic p 0 constructed in 11 do have the special unitary groups su n q as their geometric monodromy groups as conjectured therein and also prove another conjecture of 11 that predicted their arithmetic monodromy groups

nonlocal symmetries and explicit solutions for the gardner equation abstract from the known lax pair of the gardner equation the lie symmetry group method is successfully applied to find exact invariant solutions for the gardner equation with nonlocal symmetries by introducing suitable auxiliary dependent variables based on the prolonged system the explicit analytic solutions related to the jacobi elliptic functions are derived figures illustrate the interaction between the cnoidal waves and a kink wave

a novel lattice hydrodynamic model accounting for driver s memory effect and the difference of optimal velocity on curved road abstract a novel lattice hydrodynamic model is put forward which takes the effects of driver s memory and difference of optimal velocity into account on curved road linear stability analysis for the novel model is discussed and the stability condition is deduced through nonlinear analysis the mkdv equation is deduced to explore the evolution of jams near the vertex the exact solution of the mkdv equation is also derived the influence of the above two factors on traffic stability are investigated by numerical examples both numerical and analytical results demonstrate that memory effect and the difference of optimal velocity on curved road can ease traffic jams efficiently

parametrically controlling solitary wave dynamics in the modified korteweg de vries equation we demonstrate the control of solitary wave dynamics of the modified korteweg de vries mkdv equation through the temporal variations of the distributed coefficients this is explicated through exact cnoidal wave and localized soliton solutions of the mkdv equation with variable coefficients the solitons can be accelerated and their propagation can be manipulated by suitable variations of the above parameters in sharp contrast with the nonlinear schrodinger equation the soliton amplitude and widths are time independent

an extended macro traffic flow model accounting for the driver s bounded rationality and numerical tests abstract in this paper we propose a macro traffic flow model to explore the effects of the driver s bounded rationality on the evolutions of traffic waves which include shock and rarefaction waves and small perturbation and on the fuel consumption and emissions that include co hc and no x during the evolution process the numerical results illustrate that considering the driver s bounded rationality can prominently smooth the wavefront of the traffic waves and improve the stability of traffic flow which shows that the driver s bounded rationality has positive impacts on traffic flow but considering the driver s bounded rationality reduces the fuel consumption and emissions only at the upstream of the rarefaction wave while enhances the fuel consumption and emissions under other situations which shows that the driver s bounded rationality has positive impacts on the fuel consumption and emissions only at the upstream of the rarefaction wave while negative effects on the fuel consumption and emissions under other situations in addition the numerical results show that the driver s bounded rationality has little prominent impact on the total fuel consumption and emissions during the whole evolution of small perturbation

the stabilization effect of the density difference in the modified lattice hydrodynamic model of traffic flow abstract a modified lattice hydrodynamic model of traffic flow is proposed by introducing the density difference between the leading and the following lattice the stability condition of the modified model is obtained through the linear stability analysis the results show that considering the density difference leads to the stabilization of the system the burgers equation and mkdv equation are derived to describe the density waves in the stable and unstable regions respectively numerical simulations show that considering the density difference not only could stabilize traffic flow but also makes the lattice hydrodynamic model more realistic

the theoretical analysis of the lattice hydrodynamic models for traffic flow theory abstract the lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model but also connected with the microscopic car following model closely the modified korteweg de vries mkdv equation related to the density wave in a congested traffic region has been derived near the critical point since nagatani first proposed it but the korteweg de vries kdv equation near the neutral stability line has not been studied which has been investigated in detail for the car following model we devote ourselves to obtaining the kdv equation from the original lattice hydrodynamic models and the kdv soliton solution to describe the traffic jam especially we obtain the general soliton solution of the kdv equation and the mkdv equation we review several lattice hydrodynamic models which were proposed recently we compare the modified models and carry out some analysis numerical simulations are conducted to demonstrate the nonlinear analysis results

nonlinear analysis for an improved car following model account for the optimal velocity changes with memory abstract in this paper an extended car following model is developed basing on the full velocity difference model fvdm to investigate the effect of the optimal velocity changes with memory on traffic flow the stability conditions of the improved model are obtained through linear stability analysis then the time dependent ginzburg landau tdgl equation and the modified korteweg de vries mkdv equation are derived by using nonlinear analysis the kink antikink soliton can describe the traffic jams near the critical point moreover the evolution of traffic jam and corresponding the change of energy consumption are discussed numerical simulations show that the extended model is found not only to enhance the stability of traffic flow but also to depress the energy consumption the numerical results are in good agreement with the theoretical analysis

lattice hydrodynamic model with bidirectional pedestrian flow abstract the two dimensional lattice hydrodynamic model of traffic is extended to the two dimensional bidirectional pedestrian flow via taking four types of pedestrians into account the stability condition and the mkdv equation to describe the density wave of pedestrian congestion are obtained by linear stability and nonlinear analysis respectively in addition there exist three phase transitions among the freely moving phase the coexisting phase and the uniformly congested phase in the phase diagram it can also be found that the critical point a c refers to not only the fraction c 1 of the eastbound and westbound pedestrians but also the fraction c 2 of the northbound and southbound pedestrians however the critical point a c could not appear in the phase diagram and congested crowd at any time when two fractions are equal to same value of 0 5 c 1 c 2 0 5 furthermore numerical simulation is carried out to examine the performance of such a model and the results show coincidence with the theory analysis results

kink soliton characterizing traffic congestion we study traffic congestion by analyzing a one dimensional traffic flow model developing an asymptotic method to investigate the long time behavior near a critical point we derive the modified korteweg de vries mkdv equation as the lowest order model there is an infinite number of kink solitons to the mkdv equation while it has been found by numerical simulations that the kink pattern arising in traffic congestion is uniquely determined irrespective of initial conditions in order to resolve this selection problem we consider higher order corrections to the mkdv equation and find that there is a kink soliton that can deform continuously with the perturbation represented by the addition of these corrections with numerical confirmation we show that this continuously deformable kink soliton characterizes traffic congestion we also discuss the relationship between traffic congestion and the slugging phenomenon in granular flow

analytical study of vibrating systems with strong non linearities by employing saw tooth time transformations abstract a special saw tooth temporal transformation technique is formulated it is simple enough to allow analytical computation of strongly non linear free and forced dynamic responses but at the same time can be applied to the analysis of general classes of non linear problems

a multi step differential transform method and application to non chaotic or chaotic systems the differential transform method dtm is an analytical and numerical method for solving a wide variety of differential equations and usually gets the solution in a series form in this paper we propose a reliable new algorithm of dtm namely multi step dtm which will increase the interval of convergence for the series solution the multi step dtm is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations this new algorithm is applied to lotka volterra chen and lorenz systems then a comparative study between the new algorithm multi step dtm classical dtm and the classical runge kutta method is presented the results demonstrate reliability and efficiency of the algorithm developed

metastable states in a microscopic model of traffic flow it is a well known fact that metastable states of very high throughput and hysteresis effects exist in traffic flow which the simple cellular automaton model of traffic flow and its continuous generalization fail to reproduce it is shown that the model can be generalized to give a one parametric family of models a part of which reproduces the metastable states and the hysteresis the models that have that property and those that do not that are separated by a transition that can be clearly identified

breather lattice and its stabilization for the modified korteweg de vries equation we obtain an exact solution for the breather lattice solution of the modified korteweg de vries equation numerical simulation of the breather lattice demonstrates its instability due to the breather breather interaction however such multibreather structures can be stabilized through the concurrent application of ac driving and viscous damping terms

on some classes of mkdv periodic solutions we obtain exact periodic solutions of the positive and negative modified kortweg de vries mkdv equations we examine the dynamical stability of these solitary wave lattices through direct numerical simulations while the positive mkdv breather lattice solutions are found to be unstable the two soliton lattice solution of the same equation is found to be stable similarly a negative mkdv lattice solution is found to be stable we also touch upon the implications of these results for the kdv equation

a novel lattice hydrodynamic model considering the optimal estimation of flux difference effect on two lane highway abstract the optimal estimation of flux difference effect is introduced to construct a new lattice hydrodynamic model for two lane highway through linear stability analysis it is found that the new consideration plays an important influence upon the stability of two lane traffic flow moreover the mkdv equation near the critical point is derived from nonlinear analysis which describes the propagation behavior of traffic jam in two lane traffic system simulation results show that the stability of two lane traffic system can be increased and the emergence of traffic jams are effectively relieved by the optimal estimation of flux difference effect which is in good agreement with theoretical analysis

scaling behaviour in discrete traffic models we investigate the noisy discrete single lane highway traffic model proposed by nagel and schreckenberg 1992 and demonstrate by computer simulations that as a function of the car density there is a dynamical transition from laminar flow to jammed traffic in the system related to the divergence of the relaxation time of average car velocity the critical density is close to the position of the maximum in the fundamental diagram we give estimates of the critical exponents related to this jamming transition the critical density of the geometrical 1 1 dimensional percolation transition of jammed regions can be rather far from the jamming point depending on the strength of the noise which indicates that cooperativity leading to the jamming transition can be long range in character

nonlinear analysis of a new lattice hydrodynamic model with the consideration of honk effect on flux for two lane highway abstract influence of the honk on traffic flux is taken to construct a new lattice model for two lane freeway the linear stability analysis is applied to obtain the stability condition involving the honk effect on traffic flux in two lane system nonlinear analysis is implemented to get the mkdv equation for the phase transition of two lane lattice traffic flow numerical simulation is worked out to authenticate that the impact of honk on traffic flux strengthens the stability of traffic flow and suppresses the traffic congestion effectively under lane changing in two lane lattice traffic flow which is accordance with the analytic results

some characterizations of the weil representations of the symplectic and unitary groups abstract let g be a finite symplectic or unitary group we characterize the weil representations of g via their restriction to a standard subgroup then we complete the determination of complex representations of g with specific minimal polynomials of certain elements by showing that they coincide with the weil representations

the car following model considering traffic jerk abstract based on optimal velocity car following model a new model considering traffic jerk is proposed to describe the jamming transition in traffic flow on a highway traffic jerk means the sudden braking and acceleration of vehicles which has a significant impact on traffic movement the nature of the model is researched by using linear and nonlinear analysis method a thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow the time dependent ginzburg landau tdgl equation and the modified korteweg de vries mkdv equation are derived to describe the traffic flow near the critical point and the traffic jam in addition the connection between the tdgl and the mkdv equations are also given

exact solutions for a discrete system arising in traffic flow this paper concerns wave propagation in a discrete nonlinear system of equations proposed and studied by g f newell as a model for car following in traffic flow in particular newell found exact solutions for shock waves and related phenomena here exact solutions representing periodic waves and solitary waves are obtained the method relates travelling wave solutions to the toda and kac van moerbeke discrete systems in this and other ways much of the interest is in the general phenomena possible in discrete systems here including also a time lag rather than in just the specific traffic flow setting

the korteweg de vries soliton in the lattice hydrodynamic model abstract the lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model but is also closely connected with the microscopic car following model the modified korteweg de vries mkdv equation about the density wave in congested traffic has been derived near the critical point since nagatani first proposed it but the korteweg de vries kdv equation near the neutral stability line has not been studied which has been investigated in detail in the car following model so we devote ourselves to obtaining the kdv equation from the lattice hydrodynamic model and obtaining the kdv soliton solution describing the traffic jam numerical simulation is conducted to demonstrate the nonlinear analysis result

modified kdv equation for jamming transition in the continuum models of traffic abstract continuum models of traffic are proposed to describe the jamming transition in traffic flow on a highway they are the simplified versions of the hydrodynamic model of traffic two continuum models are presented one is described by the partial differential equations and the other is the discrete lattice version the linear stability theory and the nonlinear analysis are applied to the continuum models the modified korteweg de vries equation kdv near the critical point is derived using the reduction perturbation method it is shown that the jamming transition and the density wave in the congested traffic flow are described by the modified kdv equation the solutions of the kdv equations obtained from the two models are compared with that of the optimal velocity model car following model

energy consumption investigation for a new car following model considering driver s memory and average speed of the vehicles in this paper a modified car following model is proposed by taking into account the influence of the average speed effect of the vehicles and driver s memory on traffic flow basing on the two velocity difference model tvdm the stability conditions are obtained through the linear stability analysis the time dependent ginzburg landau tdgl equation and the modified korteweg de vries mkdv equation are derived in the unstable area by means of nonlinear analysis respectively the tdgland mkdv equations are constructed to describe the traffic behavior near the critical point the evolution of traffic congestion and the corresponding energy consumption are discussed numerical simulations are in good agreement with the theoretical results it is found that the extended model can not only to depress the energy consumption but also to enhance the stability of traffic flow

a new lattice model accounting for multiple optimal current differences anticipation effect in two lane system abstract this paper extends a two lane lattice hydrodynamic traffic flow model to take into account the driver s anticipation effect in sensing the multiple optimal current differences based on the proposed model we derive analytically the effect of driver s anticipation of multiple optimal current differences on the instability of traffic dynamics the phase diagrams have been plotted and discussed that the stability region enhances with anticipation effect in sensing multiple optimal current differences through simulation it is found that the oscillation of density wave around critical density decreases with an increase in lattice number and anticipation time for transient and steady state the simulation results are in good agreement with the theoretical analysis which show that considering the driver s anticipation of multiple optimal current differences in two lane lattice model stabilizes the traffic flow and suppresses the traffic jam efficiently

phase transition in a difference equation model of traffic flow a difference equation is presented to describe traffic flow on a highway the difference equation model is derived from the optimal velocity models formulated in terms of the differential equations it is compared with the differential equation models we investigate phase transitions among the freely moving phase the coexisting phase in which jams appear and the uniform congested phase the linear stability theory is applied and the neutral stability line is obtained we find the critical point below which no jams appear to derive the modified korteweg de vries equation near the critical point we apply the reductive perturbation method we also compare the nonlinear analysis result with that of the optimal velocity model it is shown that the critical point and the amplitude of the jam are different from those of the optimal velocity model

impact of the traffic interruption probability of optimal current on traffic congestion in lattice model abstract in this paper a new lattice model is proposed with the consideration of the traffic interruption probability of the optimal current the linear stability condition is obtained by linear stability analysis and the mkdv equation is deducted from nonlinear analysis via considering the traffic interruption probability of the optimal current respectively the results of numerical simulation show that the traffic interruption probability of the optimal current can efficiently suppress traffic jams under high response coefficient and deteriorate traffic situations under low response coefficient

application of a differential transformation method to strongly nonlinear damped q difference equations the theory of approximate solution lacks research on the area of nonlinear q difference equations this article explores the possibility of using the differential transformation method to find an approximate solution for strongly nonlinear damped q difference equations the time response of the nonlinear equation is presented under different parameter conditions and the results are then compared with those derived from the numerical method to verify the accuracy of the proposed method

the modified kdv equation with variable coefficients exact uni bi variable travelling wave like solutions in this paper the modified korteweg de vries mkdv equation with variable coefficients vc mkdv equation is investigated via two kinds of approaches and symbolic computation on the one hand we firstly reduce the vc mkdv equation to a second order nonlinear nonhomogeneous ode using travelling wave like similarity transformation and then we obtain its many types of exact fractional solutions with one travelling wave like variable by applying some fractional transformations to the obtained nonlinear ode on the other hand we reduce the vc mkdv equation to two nonlinear pdes with variable coefficients using the anti tangent and anti hypertangent function transformations respectively and then we given its many types of exact solutions with two different travelling wave like variables by studying the obtained nonlinear pde with variable coefficients c 2008 elsevier inc all rights reserved

nonlinear analysis for a modified continuum model considering electronic throttle et and backward looking effect abstract in this research a new car following model is developed by considering the influences of electronic throttle et dynamics and backward looking effect the improved car following model is transformed into a new continuum model through the relationship between the microscopic variables and macroscopic variables the linear stability condition of the extended continuum model can be obtained according to the linear stability theory the neutral stability curve shows that backward looking effect will improve the stability of traffic flow the kdv burgers equation is derived by the nonlinear analysis which can be used to describe the spreading behavior of traffic flow density wave in traffic congestion nearby the neutral stability line numerical experiments have been carried out including the shock waves rarefaction waves and energy consumption the numerical simulation results indicate that the traffic flow stability can be enhanced by considering et dynamics and backward looking effect in addition the above two factors can also effectively reduce energy consumption

representations of finite special linear groups in non defining characteristic we classify irreducible modules over the finite special linear group sln q in the non defining characteristic l describe restrictions of irreducible modules from gln q to sln q classify complex irreducible characters of sln q irreducible modulo l and discuss unitriangularity of the l decomposition matrix for sln q

the backward looking effect in the lattice hydrodynamic model abstract the novel lattice hydrodynamic model is presented by incorporating the backward looking effect the stability condition for the the model is obtained using the linear stability theory the result shows that considering one following site in vehicle motion leads to the stabilization of the system compared with the original lattice hydrodynamic model and the cooperative driving lattice hydrodynamic model the korteweg de vries kdv for short equation near the neutral stability line is derived by using the reductive perturbation method to show the traffic jam which is proved to be described by kdv soliton solution obtained from the kdv equation the simulation result is consistent with the nonlinear analysis

traffic jams granular flow and soliton selection the flow of traffic on a long section of road without entrances or exits can be modeled by continuum equations similar to those describing fluid flow in a certain range of traffic density steady flow becomes unstable against the growth of a cluster or phantom traffic jam which moves at a slower speed than the otherwise homogeneous flow we show that near the onset of this instability traffic flow is described by a perturbed korteweg de vries kdv equation the traffic jam can be identified with a soliton solution of the kdv equation the perturbation terms select a unique member of the continuous family of kdv solitons these results may also apply to the dynamics of granular relaxation

an extended car following model considering the self stabilizing driving behavior of headway abstract considering the self stabilizing driving behavior of headway an extended car following model called the self stabilizing optimal velocity ssov model is presented in this paper to show the effect of the self stabilizing driving behavior of headway the ssov model is investigated by the analytical and numerical methods by using the linear analysis method the stability condition of the ssov model is obtained and then by using the nonlinear analysis method the burgers kdv and modified kdv equations are respectively derived to describe the propagating behavior of traffic density wave in the stable unstable regions and near the critical point the numerical simulations are presented to show the valid of the analytical results and the effect of the self stabilizing driving behavior the analytical and numerical results all show that the self stabilizing driving behavior plays an important role on the stability and flux of the traffic flow

jamming transitions and the modified korteweg de vries equation in a two lane traffic flow abstract the two lattice models are presented to simulate the traffic flow on a two lane highway they are the lattice versions of the hydrodynamic model of traffic the one model a is described by the differential difference equation where time is a continuous variable and space is a discrete variable and the other model b is the difference equation in which both time and space variables are discrete the jamming transitions among the freely moving phase the coexisting phase and the uniform congested phase are studied by using the nonlinear analysis and the computer simulation the modified korteweg de vries mkdv equations are derived from the lattice models near the critical point the traffic jam is described by a kink antikink solution obtained from the mkdv equation it is found that the critical point the coexisting curve and the neutral stability line decrease with increasing the rate of lane changing also the computer simulation is performed for the model b it is shown that the coexisting curves obtained from the mkdv equation are consistent with the simulation result

stabilization analysis and modified korteweg de vries equation in a cooperative driving system two lattice traffic models are proposed by incorporating a cooperative driving system the lattice versions of the hydrodynamic model of traffic flow are described by the differential difference equation and difference difference equation respectively the stability conditions for the two models are obtained using the linear stability theory the results show that considering more than one site ahead in vehicle motion leads to the stabilization of the system the modified korteweg de vries equation the mkdv equation for short near the critical point is derived by using the reductive perturbation method to show the traffic jam which is proved to be described by kink anti kink soliton solutions obtained from the mkdv equations

breaking of solitary and periodic nonlinear waves abstract a nontrivial behaviour of a nonlinear wave under influence of small disturbing factors like dissipation smooth inhomogeneity of medium parameters etc is considered by the example of sine gordon equation the stage of slow adiabatic variation of the parameters of quasi stationary wave is shown to change at some finite distance due to strong instability the wave form becomes essentially non stationary breaking of stationary wave structure the breaking condition is defined by the extremum of the wave adiabatic invariant the behaviour of a wave at the nonadiabatic stage is described using a galerkin procedure

jamming transition of high dimensional traffic dynamics phase transition and critical phenomenon are investigated in high dimensional traffic flow numerically and analytically the two dimensional lattice traffic model is extended to the three and d dimensional traffic flows it is shown that the phase transition among the freely moving phase the coexisting phase and the uniformly congested phase occurs below the critical point in the two three and four dimensional traffic simulations the phase separation line and the critical point of the d dimensional traffic are consistent with those of the one dimensional traffic the time dependent ginzburg landau tdgl equation for the d dimensional traffic is derived by the use of the nonlinear analysis the phase separation line the spinodal line and the critical point are calculated from the tdgl equation it is found that the phase transition and critical phenomenon are independent of the space dimension

influence of the traffic interruption probability on traffic stability in lattice model for two lane freeway abstract in this paper a new lattice model is proposed with the traffic interruption probability term in two lane traffic system the linear stability condition and the mkdv equation are derived from linear stability analysis and nonlinear analysis by introducing the traffic interruption probability of optimal current for two lane traffic freeway respectively numerical simulation shows that the traffic interruption probability corresponding to high reaction coefficient can efficiently improve the stability of two lane traffic flow as traffic interruption occurs with lane changing

jamming transition in traffic flow on triangular lattice abstract phase transitions and critical phenomena are investigated in the two dimensional traffic flow on the triangular lattice numerically and analytically the two dimensional traffic model on the square lattice is extended to the traffic flow on the triangular lattice where the three roads cross on a site it is shown that the jamming transition between the freely moving and jammed phases depends on the configuration of car moving directions it is found that the three distinct jamming transitions occur the conventional jamming transition to the kink jams the jamming transition to the chaotic jams and the jamming transition to the oscillating jams the conventional jamming transition to the kink jams is analyzed by the use of the linear stability theory and the nonlinear method the coexisting curve between the freely moving and jammed phases is calculated from the solution of the modified korteweg de vries kdv equation

a new lattice model of traffic flow with the consideration of the traffic interruption probability abstract in this paper we present a new lattice model which involves the effects of traffic interruption probability to describe the traffic flow on single lane freeways the stability condition of the new model is obtained by the linear stability analysis and the modified korteweg de vries kdv equation is derived through nonlinear analysis thus the space will be divided into three regions stable metastable and unstable the simulation results also show that the traffic interruption probability could stabilize traffic flow

exact solutions to mkdv equation with variable coefficients abstract in this paper a special mkdv with variable coefficients is considered a transformation of variables is first applied in order to obtain a mkdv equation with constant coefficients some its one two and three soliton as well as breather type soliton solutions are derived by using hirorta s bilinear approach

the effect of headway variation tendency on traffic flow modeling and stabilization abstract advanced communications technology enables us to obtain the headway variation tendency hvt of the next moment in a car following scenario to maximize the benefits of the new technology we developed a new traffic flow model that takes into consideration the effect of hvt first linear analysis method is used to derive the linear stability condition that determines whether the hvt can improve traffic system stability then using the reductive perturbation method a modified kdv mkdv equation is obtained and the kink antikink solutions are derived the phase diagram of driver sensitivity against equilibrium headway is also plotted by using the neutral stability line derived from linear analysis and the coexisting line derived from nonlinear analysis this diagram demonstrates that hvt does have the ability to improve the stability of traffic stream finally the effect of hvt is validated through numerical simulations where it is evident that the information of hvt can smooth the traffic stream and prevent the formation of traffic congestion

soliton solutions backlund transformation and wronskian solutions for the extended 2 1 dimensional konopelchenko dubrovsky equations in fluid mechanics abstract this paper is to investigate the extended 2 1 dimensional konopelchenko dubrovsky equations which can be applied to describing some phenomena in the stratified shear flow the internal and shallow water waves and plasmas bilinear form equations are transformed from the original equations and n soliton solutions are derived via symbolic computation bilinear form backlund transformation and single soliton solution are obtained and illustrated wronskian solutions are constructed from the backlund transformation and single soliton solution

solitary wave transformation in a medium with sign variable quadratic nonlinearity and cubic nonlinearity abstract solitary wave transformation in a zone with a sign variable coefficient for the quadratic nonlinear term is studied in the framework of the variable coefficient extended korteweg de vries equation this situation can be realised for internal waves in a stratified ocean when the pycnocline lies midway between the sea bed and the sea surface the effects of the cases when the coefficient of the cubic nonlinear term can be either positive or negative are investigated for small amplitude solitary waves previous results when the cubic nonlinear term is ignored are confirmed the initial solitary wave is destroyed and solitary waves of the opposite polarity are generated after passage through the turning point i e the location where the coefficient of the quadratic nonlinear term is zero for large amplitude solitary waves the cubic nonlinear term and particularly its sign influence significantly both the polarity and amplitude of the resulting solitary waves if the cubic nonlinear term has a negative coefficient the amplitude of the large terminal wave is comparable with the initial value it is less than 50 when the cubic nonlinear term is ignored if the cubic nonlinear term has a positive coefficient the result depends on the initial wave amplitude large amplitude solitary waves pass through the transition zone keeping the solitary wave shape and its polarity moderate amplitude solitary wave are destroyed and transformed to a strongly pulsating wave packet breather

discrete stochastic models for traffic flow we investigate a probabilistic cellular automaton model which has been introduced recently this model describes single lane traffic flow on a ring and generalizes the asymmetric exclusion process models we study the equilibrium properties and calculate the so called fundamental diagrams flow versus density for parallel dynamics this is done numerically by computer simulations of the model and by means of an improved mean field approximation which takes into account short range correlations for cars with a maximum velocity of 1 the simplest nontrivial approximation gives the exact result for higher velocities the analytical results obtained by iterated application of the approximation scheme are in excellent agreement with the numerical simulations

application of the differential transformation method to the solution of a damped system with high nonlinearity abstract this paper employs the differential transformation method to investigate the response of a damped system with high nonlinearity the accuracy and validity of the proposed method are demonstrated through its application to the solution of a dynamic system with various values of power form nonlinearity the numerical results indicate that the amplitude decays more rapidly at higher values of nonlinearity particularly at higher values of the damping coefficient it is shown that the current results are in excellent agreement with those provided by the runge kutta method therefore the method presented in this study provides an effective scheme for determining the solutions of a damped vibration problem with high nonlinearity

time dependent ginzburg landau equation in a car following model considering the driver s physical delay abstract in this paper an extended car following model considering the delay of the driver s response in sensing headway is proposed to describe the traffic jam it is shown that the stability region decreases when the driver s physical delay in sensing headway increases the phase transition among the freely moving phase the coexisting phase and the uniformly congested phase occurs below the critical point by applying the reductive perturbation method we get the time dependent ginzburg landau tdgl equation from the car following model to describe the transition and critical phenomenon in traffic flow we show the connection between the tdgl equation and the mkdv equation describing the traffic jam

an extended continuum model considering optimal velocity change with memory and numerical tests in this paper an extended continuum model of traffic flow is proposed with the consideration of optimal velocity changes with memory the new model s stability condition and kdv burgers equation considering the optimal velocities change with memory are deduced through linear stability theory and nonlinear analysis respectively numerical simulation is carried out to study the extended continuum model which explores how optimal velocity changes with memory affected velocity density and energy consumption numerical results show that when considering the effects of optimal velocity changes with memory the traffic jams can be suppressed efficiently both the memory step and sensitivity parameters of optimal velocity changes with memory will enhance the stability of traffic flow efficiently furthermore numerical results demonstrates that the effect of optimal velocity changes with memory can avoid the disadvantage of historical information which increases the stability of traffic flow on road and so it improve the traffic flow stability and minimize cars energy consumptions

solitary wave solutions for time fractional third order modified kdv equation using two reliable techniques g g expansion method and improved g g expansion method abstract in the present paper we construct the analytical exact solutions of a nonlinear evolution equation in mathematical physics namely time fractional modified kdv equation by using g g expansion method and improved g g expansion method as a result new types of exact analytical solutions are obtained

nonautonomous mixed mkdv sinh gordon hierarchy the construction of a nonautonomous mixed mkdv sine gordon model is proposed by employing an infinite dimensional affine lie algebraic structure within the zero curvature representation a systematic construction of soliton solutions is provided by an adaptation of the dressing method which takes into account arbitrary time dependent functions a particular choice of those arbitrary functions provides an interesting solution describing the transition of a pure mkdv system into a pure sine gordon soliton

group representations and lattices this paper began as an attempt to understand the euclidean lattices that were recently constructed using the theory of elliptic curves by elkies e and shioda shl sh2 from the point of view of group representations the main idea appears in a note of thompson th2 if one makes strong irreducibility hypotheses on a rational representation v of a finite group g then the g stable euclidean lattices in v are severely restricted unfortunately these hypotheses are rarely satisfied when v is absolutely irreducible over q but there are many examples where the ring endg v is an imaginary quadratic field or a definite quaternion algebra these representations allow us to construct some of the mordell weil lattices considered by elkies and shioda as well as some interesting even unimodular lattices that do not seem to come from the theory of elliptic curves in 1 we discuss lattices and hermitian forms on y7 and in 2 4 the strong irreducibility hypotheses we wish to make in 5 we show how our hypotheses imply the existence of a finite number up to isomorphism of euclidean z g lattices l in v with endg l a maximal order in endg v we give some examples with dim v 8 in 6 and in 7 9 discuss the invariants of l such as the dual lattice and theta function the rest of the paper is devoted to examples in most g is a finite group of lie type and v is obtained as an irreducible summand of the weil representation of g some of the representation theoretic problems left open by this paper are to find all examples of pairs g v satisfying the strong irreducibility hypotheses of 2 4 and to determine the invariants shortest nonzero vector theta function thompson series of the g lattices l so effortlessly constructed inside v

the impact of the density difference memory integral on traffic stability in two lane lattice hydrodynamic model abstract the density difference memory integral ddmi term can be applied to describe traffic density information of the driver s historical memory during a continuous period of time in this paper a new lattice model is provided with the consideration of the ddmi effect for two lane freeway the linear stability condition of two lanes has been derived by considering the ddmi effect through linear stability theory which shows that the ddmi effect can improve traffic stability under lane changing according to the observation of simulation the ddmi effect conduces to the stability of traffic flow for two lane freeway

a lattice hydrodynamic model based on delayed feedback control considering the effect of flow rate difference abstract in this paper a lattice hydrodynamic model is derived considering not only the effect of flow rate difference but also the delayed feedback control signal which including more comprehensive information the control method is used to analyze the stability of the model furthermore the critical condition for the linear steady traffic flow is deduced and the numerical simulation is carried out to investigate the advantage of the proposed model with and without the effect of flow rate difference and the control signal the results are consistent with the theoretical analysis correspondingly

derivation and empirical validation of a refined traffic flow model abstract the gas kinetic foundation of fluid dynamic traffic equations suggested in previous papers d helbing physica a 219 1995 375 and 391 is further refined by applying the theory of dense gases and granular materials to the boltzmann like traffic model by paveri fontana it is shown that despite the phenomenologically similar behaviour or ordinary and granular fluids the relations for these cannot directly be transferred to vehicular traffic the dissipative and anisotropic interactions of vehicles as well as their velocity dependent space requirements lead to a considerably different structure of the macroscopic traffic equations also in comparison with the previously suggested traffic flow models as a consequence the instability mechanisms of emergent density waves are different crucial assumptions are validated by empirical traffic data and essential results are illustrated by figures

rigid local systems and finite general linear groups we use hypergeometric sheaves on mathbb g m mathbb f q which are particular sorts of rigid local systems to construct explicit local systems whose arithmetic and geometric monodromy groups are the finite general linear groups mathrm gl n q for any n ge 2 and any prime power q so long as q 3 when n 2 this paper continues a program of finding simple in the sense of simple to remember families of exponential sums whose monodromy groups are certain finite groups of lie type cf gross adv math 224 2531 2543 2010 katz mathematika 64 785 846 2018 and katz and tiep finite fields appl 59 134 174 2019 adv math 358 106859 2019 proc lond math soc 2020 for certain finite symplectic and unitary groups or certain sporadic groups cf katz and rojas leon finite fields appl 57 276 286 2019 and katz et al j number theory 206 1 23 2020 int j number theory 16 341 360 2020 trans am math soc 373 2007 2044 2020 the novelty of this paper is obtaining mathrm gl n q in this hypergeometric way a pullback construction then yields local systems on mathbb a 1 mathbb f q whose geometric monodromy groups are mathrm sl n q these turn out to recover a construction of abhyankar

effect of optimal estimation of flux difference information on the lattice traffic flow model abstract in this paper a new lattice model is proposed by considering the optimal estimation of flux difference information the effect of this new consideration upon the stability of traffic flow is examined through linear stability analysis furthermore a modified korteweg de vries mkdv equation near the critical point is constructed and solved by means of nonlinear analysis method and thus the propagation behavior of traffic jam can be described by the kink antikink soliton solution of the mkdv equation numerical simulation is carried out under periodical condition with results in good agreement with theoretical analysis therefore it is verified that the new consideration can enhance the stability of traffic systems and suppress the emergence of traffic jams effectively

hyperelliptic solutions of modified korteweg de vries equation of genus g essentials of the miura transformation explicit hyperelliptic solutions of the modified korteweg de vries equations without any ambiguous parameters were constructed in terms of only the hyperelliptic al functions over the non degenerate hyperelliptic curve y2 f x of arbitrary genus g in the derivation any functions or baker akhiezer functions were not essentially used then the miura transformation naturally appears as the connection between the hyperelliptic functions and hyperelliptic al functions

research on preceding vehicle s taillight effect and energy consumption in an extended macro traffic model abstract in this paper a modified continuum model considering the vehicle s taillight effect is presented the high order fluid dynamics model of taillight effect is derived by means of the transformation from micro to macro combined with the continuous conservation equation of traffic flow the linear and nonlinear analysis of the new macroscopic hydrodynamic model is carried out the linear analysis proves that the model has the characteristics of heterogeneity and the stability condition of traffic flow is obtained kdv burgers equations describing the qualitative characteristics of density waves are obtained by nonlinear analysis and the corresponding density wave solutions are obtained numerical simulation results show that the unstable state region of the macro model with taillight effect is shrinking in addition the energy consumption of the model is simulated numerically and the results show that the energy consumption of the vehicle is reduced by considering the taillight effect therefore we believe that the taillight effect is beneficial to traffic flow stability and reduce energy consumption

nonlinear analysis for a modified continuum model considering driver s memory and backward looking effect abstract account for the integral form of optimal velocity changes with memory and backward looking effect an extended car following model is proposed in this paper through the relation between macro and micro variables the extended car following is transformed to a new continuum model according to the linear stability theory the linear stability s condition of the presented model is obtained the modified kdv burgers equation is established through non linear analysis to describe the spreading behavior of the traffic density wave near the neutral stability line the numerical simulation results show that the backward looking effect can improve the traffic flow s stability and the integral form of optimal velocity changes with memory can relieve the traffic congestion

gas kinetic derivation of navier stokes like traffic equations macroscopic traffic models have recently been severely criticized to base on lax analogies only and to have a number of deficiencies therefore this paper shows how to construct a logically consistent fluid dynamic traffic model from basic laws for the acceleration and interaction of vehicles these considerations lead to the gas kinetic traffic equation of paveri fontana its stationary and spatially homogeneous solution implies equilibrium relations for the fundamental diagram the variance density relation and other quantities which are partly difficult to determine empirically paveri fontana s traffic equation allows the derivation of macroscopic moment equations which build a system of non closed equations this system can be closed by the well proved method of chapman and enskog which leads to euler like traffic equations in zeroth order approximation and to navier stokes like traffic equations in first order approximation the latter are finally corrected for the finite space requirements of vehicles it is shown that the resulting model is able to withstand the above mentioned criticism

jamming transitions and the effect of interruption probability in a lattice traffic flow model with passing abstract a new lattice hydrodynamic model is proposed by considering the interruption probability effect on traffic flow with passing and analyzed both theoretically and numerically from linear and non linear stability analysis the effect of interruption probability on the phase diagram is investigated and the condition of existence for kink antikink soliton solution of mkdv equation is derived the stable region is enhanced with interruption probability and the jamming transition occurs from uniform flow to kink flow through chaotic flow for higher and intermediate values of non interruption effect of passing it is also observed that there exists conventional jamming transition between uniform flow and kink flow for lower values of non interruption effect of passing numerical simulations are carried out and found in accordance with the theoretical findings which confirm that the effect of interruption probability plays an important role in stabilizing traffic flow when passing is allowed

delay effect on phase transitions in traffic dynamics a dynamical model of traffic is proposed to take into account the effect of acceleration delay in the limit of no delay the model reproduces the optimal velocity model of traffic when the delay is small it is shown that the phase transition among the freely moving phase the coexisting phase and the uniform congested phase occurs below the critical point above the critical point no phase transition occurs the value a c of the critical point increases with increasing delay time 1 b where a is the friction coefficient or sensitivity parameter when the delay time is longer than frac 1 2 the critical point disappears and the phase transition always occurs the linear stability theory and nonlinear analysis are applied the critical point predicted by the linear stability theory agrees with the simulation result the modified korteweg de vries kdv equation is obtained from the nonlinear analysis near the critical point the phase separation line obtained from the modified kdv equation is consistent with the simulation result