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

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

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

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

identification of nonminimum phase fir systems using the third and fourth order cumulants an algorithm is proposed for ma system identification using the third and fourth order cumulants asymmetric non gaussian input and gaussian measurement noise are assumed simulation results show that the proposed algorithm is useful when the characteristics of noise are not known or when the snr is low

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

blind identification of hammerstein channels using qam psk and ofdm inputs this paper is concerned with the blind identification of passband and baseband hammerstein channels using cumulants of the received sequence the channel is excited by common communication signals such as qam psk and ofdm sparseness of the higher order cumulant lags is exploited exact expressions and algorithms involving the output cumulants are developed performance is assessed by simulations

hybrid port hamiltonian systems from parameterized incidence matrices to hybrid automata abstract this paper shows how to formally design a hybrid automaton model for a wide class of dissipative physical systems with sources and switching topology this method is based on a mathematical representation of the dynamic network graph and of its dual graph using the hybrid incidence matrix and on a constructive method for analyzing admissible and constrained configurations the port hamiltonian representation associated with the set of hybrid system configurations parameterized by the discrete state of the switches is synthesized to be part of the hybrid automaton of the system this is a further step towards a generic control synthesis for physical switching systems

deconvolution and estimation of transfer function phase and coefficients for nongaussian linear processes nongaussian linear processes are considered it is shown that the phase of the transfer function can be estimated under broad conditions this is not true of gaussian linear processes and in this sense gaussian linear processes are atypical the asymptotic behavior of a phase estimate is determined the phase estimates make use of bispectral estimates these ideas are applied to a problem of deconvolution which is effective even when the transfer function is not minimum phase a number of computational illustrations are given

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

cumulant based order determination of non gaussian arma models the objective is the order determination of non gaussian and nonminimum phase autoregressive moving average arma models using higher order cumulant statistics the two methods developed assume knowledge of upper bounds on the arma orders the first method performs a linear dependence search among the columns of a higher order statistics matrix by means of the gram schmidt orthogonalization procedure in the second method the order of the ar part is found as the rank of the matrix formed by the higher order statistics sequence for numerically robust rank determination the singular value decomposition approach is adopted the argument principle and samples of the polyspectral phase are used to obtain the relative degree of the arma model from which the order of the ma part can be determined statistical analysis is included for determining the correct ma order with high probability when estimates of third order cumulants are only available simulations are used to verify the performance of the methods and compare autocorrelation with cumulant based order determination approaches

identification of non minimum phase linear stochastic systems abstract the identification of time invariant non minimum phase stochastic systems driven by non gaussian white noise is considered given only the noisy observations of the system output a two step procedure is proposed in the first step a spectrally equivalent system is estimated using a standard technique that exploits only the second order statistics of the measurements in the second step a partial set of 4th order cumulants of the measurements is exploited to resolve the location of the system zeros knowledge of the probability distribution of the driving noise is not required strong consistency of the proposed estimator is proved under certain sufficient conditions simulation results are also presented in support of the theory

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

blind equalization of nonminimum phase channels higher order cumulant based algorithm higher order cumulant analysis is applied to the blind equalization of linear time invariant lti nonminimum phase channels the channel model is moving average based to identify the moving average parameters of channels a higher order cumulant fitting approach is adopted in which a novel relay algorithm is proposed to obtain the global solution in addition the technique incorporates model order determination the transmitted data are considered as independently identically distributed random variables over some discrete finite set e g set or 1 or 3 a transformation scheme is suggested so that third order cumulant analysis can be applied to this type of data simulation examples verify the feasibility and potential of the algorithm performance is compared with that of the noncumulant based sato scheme in terms of the steady state mse and convergence rate

higher order spectrum estimation via noncausal autoregressive modeling and deconvolution a method for nonminimum phase finite impulse response fir system identification is introduced that is based on noncausal autoregressive ar modeling of the third moments of the output data the magnitude and phase response of the fir system are expressed in terms of the parameters of a noncausal ar model the set of ar parameters is obtained by solving an overdetermined linear system of equations that is formed using third moment estimates of the output data the performance of the method is illustrated with simulation examples

order reduction of siso nonminimum phase stochastic systems we consider the order reduction problem for single input single output nonminimum phase linear stochastic systems the problem is formulated as that of approximating the original system output process by another stochastic process generated via a reduced order model it is shown that in order to obtain a correct phase approximation it is necessary to consider some higher order statistics of the original process in addition to the usual second order statistics a computationally feasible approximation criterion is proposed and analyzed an example is also presented to illustrate the proposed method

identification of nonminimum phase systems using higher order statistics a method is presented for identification of linear time variant nonminimum phase systems when only output data are available the input sequence need not be independent but it must be non gaussian with some special properties described in the test the authors model a finite dimensional system as an arma autoregressive moving average rational function of known orders but the special cases of ar ma and all pass models are also considered to estimate the parameters of their model the authors utilize both second and higher order statistics of the output which may be contaminated by additive zero mean gaussian white noise of unknown variance the parameter estimators obtained are proved under mild conditions to be consistent simulations verify the performance of the proposed method in the case of relatively low signal to noise ratios and when there is a model order mismatch

maximum likelihood joint channel and data estimation using genetic algorithms a batch blind equalization scheme is developed based on maximum likelihood joint channel and data estimation in this scheme the joint maximum likelihood optimization is decomposed into a two level optimization loop a micro genetic algorithm is employed at the upper level to identify the unknown channel model and the viterbi algorithm is used at the lower level to provide the maximum likelihood sequence estimation of the transmitted data sequence as is demonstrated in simulation the proposed method is much more accurate compared with existing algorithms for joint channel and data estimation

a dual relation between port hamiltonian systems and the brayton moser equations for nonlinear switched rlc circuits in the last decades several researchers have concentrated on the dynamic modeling of nonlinear electrical circuits from an energy based perspective a recent perspective is based on the concept of port hamiltonian ph systems in this paper we discuss the relations between the classical brayton moser bm equations stemming from the early sixties and ph models for topologically complete nonlinear rlc circuits with and without controllable switches it will be shown that ph systems precisely dualize the bm equations leading to possible advantages at the level of controller design consequently useful and important properties of the one framework can be translated to the other control designs for the ph model cannot be directly implemented since they require observation of flux and charges which are not directly available through standard sensors while the bm models require only observation of currents and voltages the introduced duality allows to pull back ph designs to the space of currents and voltages this offers the possibility to exchange several different techniques available in the literature for modeling analysis and controller design for rlc circuits illustrative examples are provided to emphasize the duality between both frameworks

adaptive deconvolution and identification of nonminimum phase fir systems based on cumulants a novel adaptive deconvolution and system identification scheme is introduced for a linear non minimum phase finite impulse response fir system driven by non gaussian white noise the adaptive scheme is based on approximating the fir system by noncausal autoregressive ar models and using higher order cumulants of the system output as such it is a blind equalization deconvolution scheme the set of updated ar parameters is obtained by using a gradient type algorithm and by using higher order cumulants instead of time samples of the output signal it is demonstrated by means of extensive simulations that the adaptive scheme works well for both stationary and nonstationary cases as expected it outperforms the autocorrelation based gradient method for nonminimum phase system identification and deconvolution performance comparisons to existing methods are given using as figures of merit the probability of errors in the restored input sequence computational complexity and convergence rate

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

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

multi stage blind clustering equaliser a multi stage blind clustering algorithm is proposed for equalisation of multi level quadrature amplitude modulation m qam channels a hierarchical decomposition divides the task of equalising a high order qam channel into much simpler sub tasks each sub task can be accomplished fast and reliably using a blind clustering algorithm derived originally for 4 qam signals the constant modulus algorithm cma is used as a benchmark to assess this multi stage blind equaliser it is demonstrated that the new blind algorithm achieves much faster convergence and is very robust when input symbols are not sufficiently white this multi stage clustering equaliser only requires slightly more computations than the cma and like the latter its computational complexity does not increase as the levels of digital symbols increase

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

lagrangian modeling of switching electrical networks in this paper a general and systematic method is presented to model topologically complete electrical networks with or without multiple or single switches within the euler lagrange framework apart from the physical insight that can be obtained in this way the framework has proven to be useful for the application of passivity based control techniques which on a case by case basis already has shown to be useful for the control of power converters within the class of switching electrical networks the switches are assumed to be ideal and pulse width modulation is taken into account magnetic coupling of inductive elements is also included in the framework

control by interconnection and standard passivity based control of port hamiltonian systems the dynamics of many physical processes can be suitably described by port hamiltonian ph models where the importance of the energy function the interconnection pattern and the dissipation of the system is underscored to regulate the behavior of ph systems it is natural to adopt a passivity based control pbc perspective where the control objectives are achieved shaping the energy function and adding dissipation in this paper we consider the pbc techniques of control by interconnection cbi and standard pbc in cbi the controller is another ph system connected to the plant through a power preserving interconnection to add up their energy functions while in standard pbc energy shaping is achieved via static state feedback in spite of the conceptual appeal of formulating the control problem as the interaction of dynamical systems the current version of cbi imposes a severe restriction on the plant dissipation structure that stymies its practical application on the other hand standard pbc which is usually derived from a uninspiring and non intuitive ldquopassive output generationrdquo viewpoint is one of the most successful controller design techniques the main objectives of this paper are 1 to extend the cbi method to make it more widely applicable in particular to overcome the aforementioned dissipation obstacle 2 to show that various popular variants of standard pbc can be derived proceeding from a unified perspective 3 to establish the connections between cbi and standard pbc proving that the latter is obtained restricting the former to a suitable subset providing a nice geometric interpretation to standard pbc and comparing the size of the set of ph plants for which they are applicable

power based control canonical coordinate transformations integral and adaptive control power based modeling was originally developed in the early sixties to describe a large class of nonlinear electrical rlc networks in a special gradient form recently this idea has been extended for modeling and control of a larger class of physical systems in this paper first coordinate transformations are introduced for systems described in this framework such that the physical structure is preserved such a transformation can provide new insights for both analysis and control design second power based integral and adaptive control schemes are presented advantages of these schemes are shown by their application on standard mechanical systems

a hamiltonian viewpoint in the modeling of switching power converters in this paper we show how using the hamiltonian formalism we can systematically derive mathematical models that describe the behaviour of a large class of switching power converters including the boost buck buck boost cuk and flyback converters we follow the approach proposed by van der schaft and maschke and extract from the basic energy conserving lc circuit the remaining elements i e resistors switches diodes and transformers which we treat as external ports this method naturally yields a hamiltonian system with two additional conjugated sets of port variables this procedure besides being systematic and very general has the additional advantage of resulting in equations of a form appropriate for simulation and design of the highly succesful passivity based controllers

a new order determination technique for arma processes it is generally recognized that when performing spectral estimation via the modeling approach autoregressive moving average arma models can provide estimates of higher resolution than auto gressive models alone 1 2 however there is lacking a systematic method for determining the orders of an arma process from its output of the very few order determination techniques in existence most are trial and error based the akaike information criterion for arma processes is one such example this paper presents a new method that determines the arma orders in one pass it is a modification of the method of chow 6 and uses the gram schmidt orthonormalization procedure to determine linear dependency of the columns in an order determination the theoretical development is verified by simulation which also includes results on order determination from output sequences alone

arma bispectrum approach to nonminimum phase system identification an identification procedure is proposed for a nongaussian white noise driven linear time invariant nonminimum phase fir finite impulse response system the method is based on parametric modeling of the third moments of the output sequence and uses causal and anticausal autoregressive moving average arma models the magnitude and phase response of the system are expressed in terms of the ar parameters of the arma models in particular the ar part of the causal arma model captures the minimum phase component of the system and the ar part of the anticausal arma captures the maximum phase component both sets of parameters are obtained by solving overdetermined linear systems of equations a model order selection criterion based on third order moments is proposed the arma bispectrum approach is compared to more conventional approaches for magnitude and phase reconstruction it is demonstrated that the proposed identification procedure exhibits improved modeling performance the method does not require knowledge of the non gaussian noise distribution

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

closed form recursive estimation of ma coefficients using autocorrelations and third order cumulants the authors derive a simple recursive closed form algorithm for estimating the parameters of a moving average ma model of known order using only the autocorrelation and the 1 d diagonal slice of the third order cumulant of its response to excitation by an unobservable non gaussian iid process the output may be corrupted by zero mean nonskewed white noise of unknown variance the autoregressive moving average arma case is briefly discussed

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

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

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

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