an application for a modified kdv equation by the decomposition method and finite element method a numerical solution to a modified korteweg de vries mkdv equation is obtained using a lumped galerkin method with quadratic b spline finite element method fem and using the adomian s decomposition method adm test problems concerning the motion and interaction of soliton solutions are used to compare the fem with the adm classical problems concerning the development motion and interaction of solitons are used to validate the methods the present methods extremely well in terms of accuracy efficiency simplicity stability and reliability

classification of systems of nonlinear ordinary differential equations with superposition principles a system of n first order nonlinear ordinary differential equations x t f x t is said to admit a superposition principle if its general solution can be written as a function of a finite number m of particular solutions and n constants such a system can be associated with the nonlinear action of a lie group g on a space m we show that indecomposable systems of ode s with supersposition principles are obtained if and only if the lie algebras l0 l corresponding to the isotropy group h of a point and the group g respectively define a transitive primitive filtered lie algebra l l0 using known results from the theory of transitive primitive lie algebras we deduce that l0 must be a maximal subalgebra of l and that g must be an affine group a simple lie group or the direct product of two identical simple lie groups affine groups lead to linear equations the other types to nonlinear equations with polynomial or rational nonlinearities equations corresponding to the classical complex lie algebra

a new approach for the application of adomian decomposition method for the solution of fractional space diffusion equation with insulated ends abstract this paper presents the new approach for the solution of the space fractional diffusion equation defined in finite domain by adomian decomposition method adm a typical example of special interest with fractional space derivative of order 1 2 is considered in the present analysis and solved by adm after expressing the initial condition as fourier series the explicit solution of the space fractional diffusion equation has been presented in the closed form and then the numerical solution has been represented graphically the behaviour of adomian solutions and the effects of different values of are shown graphically

on experimental results and explicit exact solutions for the generalized boussinesq type equation we implemented a decomposition method for approximating the solution of the generalized boussinesq type equation by using this scheme the explicit exact solution is calculated in the form of a convergent power series with easily computable components to illustrate the application of this method numerical results are derived by using the calculated components of the decomposition series the obtained results are found to be in good agreement with the exact solution

reduction by invariants and projection of linear representations of lie algebras applied to the construction of nonlinear realizations a procedure for the construction of nonlinear realizations of lie algebras in the context of vessiot guldberg lie algebras of first order systems of ordinary differential equations odes is proposed the method is based on the reduction of invariants and projection of lowest dimensional irreducible representations of lie algebras applications to the description of parameterized first order systems of odes related by contraction of lie algebras are given in particular the kinematical lie algebras in 2 1 and 3 1 dimensions are realized simultaneously as vessiot guldberg lie algebras of parameterized nonlinear systems in r3 and r4 respectively

new explicit exact solutions for the generalized coupled hirota satsuma kdv system in this paper we study the generalized coupled hirota satsuma kdv system by using the two new improved projective riccati equations method as a result many explicit exact solutions which contain new solitary wave solutions periodic wave solutions and combined formal solitary wave solutions and combined formal periodic wave solutions are obtained

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

conditions for strict distinguishability of single output nonlinear control affine systems abstract strict distinguishability is the property of two systems to generate identical output signals only for the zero control input and the zero initial state vector the objective of this paper is to characterize this property for single output nonlinear control affine systems in this context we first introduce the indistinguishability zone of the systems this zone represents the set of control inputs and initial state vectors that make the output signals of the systems indistinguishable the explicit identification of the elements of this set is proposed in the paper from this result necessary and sufficient conditions for strict distinguishability are then established under suitable assumptions

a new class of integrable systems we present a family of dynamical systems associated with the motion of a particle in two space dimensions these systems possess a second integral of motion quadratic in velocities apart from the hamiltonian and are thus completely integrable they were found through the derivation and subsequent resolution of the integrability condition in the form of a partial differential equation pde for the potential a most important point is that the same pde was derived through considerations on the analytic structure of the singularities of the solutions weak painleve property

the fundamental group of the quillen complex of the symmetric group abstract in this paper we investigate the fundamental group of the quillen complex of the symmetric group a p s n we show that when p is an odd prime the simplicial complex a p s n is simply connected if and only if 3 p 2 n p 2 or n p 2 p furthermore we determine the fundamental group 1 a p s n in all cases except those where p 5 and n 3 p 3 p 1 and that where p 3 and n 10

solitary wave solutions for compound kdv type and compound kdv burgers type equations with nonlinear terms of any order in this letter based on the idea of adomian s decomposition method and with help of mathematica we obtain the exact solutions for compound kdv type and compound kdv burgers type equations with nonlinear terms of any order in this paper by considering the decomposition scheme we first obtain the exact solutions of these two equation for the initial conditions without using any classical transformations and then their numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions their remarkable accuracy is finally demonstrated in the study of some values p 1 of the compound kdv type and compound kdv burgers type equations

nonlinear superposition formulae based on the lie group so n 1 n systems of nonlinear ordinary differential equations are constructed for which the general solution is algebraically expressed in terms of a finite number of particular solutions expressions of that type are called nonlinear superposition formulae these systems are connected with local lie group transformations on their homogeneous spaces in the work presented here the nonlinear superposition formulae are constructed for the case of the so 3 2 group and some aspects of the general case of so n 1 n are studied

comparison of the solutions obtained by b spline fem and adm of kdv equation a numerical solution to a generalized korteweg de vries kdv equation is obtained using the galerkin method with quadratic b spline finite element method fem over which the nonlinear term is locally linearized and using the adomian s decomposition method adm test problems concerning the motion and interaction of soliton solutions are used to compare the fem with the adm the present methods extremely well in terms of accuracy efficiency simplicity stability and reliability

direct approach to the periodic solutions of the multidimensional sine gordon equation a number of identities for multidimensional theta functions and their derivatives are derived application to the nonlinear partial differential equations is exemplified for the sine gordon equation in consequence the multidimensional sine gordon equation can be reduced to a functional equation and then to a set of algebraic equations several particular cases are also discussed

invertibility of switched nonlinear systems this article addresses the invertibility problem for switched nonlinear systems affine in controls the problem is concerned with reconstructing the input and switching signal uniquely from given output and initial state we extend the concept of switch singular pairs introduced recently to nonlinear systems and develop a formula for checking if the given state and output form a switch singular pair a necessary and sufficient condition for the invertibility of switched nonlinear systems is given which requires the invertibility of individual subsystems and the nonexistence of switch singular pairs when all the subsystems are invertible we present an algorithm for finding switching signals and inputs that generate a given output in a finite interval when there is a finite number of such switching signals and inputs detailed examples are included to illustrate these newly developed concepts

the sine gordon equations complete and partial integrability the sine gordon equation in one space one time dimension is known to possess the painleve property and to be completely integrable it is shown how the method of singular manifold analysis obtains the backlund transform and the lax pair for this equation a connection with the sequence of higher order kdv equations is found the modified sine gordon equations are defined in terms of the singular manifold these equations are shown to be identically painleve also certain rational solutions are constructed iteratively the double sine gordon equation is shown not to possess the painleve property however if the singular manifold defines an affine minimal surface then the equation has integrable solutions this restriction is termed partial integrability the sine gordon equation in n 1 variables n space 1 time where n is greater than one is shown not to possess the painleve property the condition of partial integrability requires the singular manifold to be an einstein space with null scalar curvature the known integrable solutions satisfy this constraint in a trivial manner finally the coupled kdv or hirota satsuma equations possess the painleve property the associated modified equations are derived and from these the lax pair is found

normal form solutions of dynamical systems in the basin of attraction of their fixed points abstract the normal form theory of poincare siegel and arnol d is applied to an analytically solvable lotka volterra system in the plane and a periodically forced dissipative duffing s equation with chaotic orbits in its 3 dimensional phase space for the planar model we determine exactly how the convergence region of normal forms about a nodal fixed point is limited by the presence of singularities of the solutions in the complex t plane despite such limitations however we show in the case of a periodically driven system that normal forms can be used to obtain useful estimates of the basin of attraction of a stable fixed point of the poincare map whose boundary is formed by the intersecting invariant manifolds of a second hyperbolic fixed point nearby

link between solitary waves and projective riccati equations many solitary wave solutions of nonlinear partial differential equations can be written as a polynomial in two elementary functions which satisfy a projective hence linearizable riccati system from that property the authors deduce a method for building these solutions by determining only a finite number of coefficients this method is much shorter and obtains more solutions than the one which consists of summing a perturbation series built from exponential solutions of the linearized equation they handle several examples for the henon heiles hamiltonian system they obtain several exact solutions one of them defines a new solitary wave solution for a coupled system of boussinesq and nonlinear schrodinger equations for a third order dispersive equation with two monomial nonlinearities they isolate all cases where the general solution is single valued

simple homotopy types and finite spaces whitehead s theory of simple homotopy types is inspired by tietze s theorem in combinatorial group theory which states that any finite presentation of a group could be deformed into any other by a finite sequence of elementary moves which are now called tietze transformations whitehead translated these algebraic moves into the well known geometric moves of elementary collapses and expansions of finite simplicial complexes

superposition principles for matrix riccati equations a superposition rule is obtained for the matrix riccati equation mre w a wb cw wdw where w t a t b t c t and d t are real n n matrices expressing the general solution in terms of five known solutions for all n 2 the symplectic mre w wt a at d dt c bt is treated separately and a superposition rule is derived involving only four known solutions for the unitary and gl n r subcases with d a and c bt or d a and c bt respectively superposition rules are obtained involving only two solutions the derivation of these results is based upon an interpretation of the mre in terms of the action of the groups sl 2n r sp 2n r u n and gl n r on the grassman manifold gn r2n

systems of ordinary differential equations with nonlinear superposition principles abstract this work is concerned with the derivation of superposition rules which express the general solution of ordinary differential equations x x t x r n t r in terms of a finite number of particular solutions the point of departure is lie s criterion according to which such a rule exists if and only if the vector fields x t generate a finite dimensional lie algebra we provide three different constructive methods for deriving superposition rules and apply them to systems of coupled riccati equations of the projective and conformal types based respectively on the lie algebra sl n 1 r and o p 1 n p 1

the pinney equation and its discretization the pinney equation is part of the original ermakov system which has been the subject of intensive study recently here we show that it may be related to a two dimensional conformal riccati equation leading to a new method for its linearization a discrete analogue of the pinney equation is constructed using the above connection with the conformal group an alternative discretization is obtained by using a discrete schwarz derivative both of these nonlinear difference equations are linearizable

the structures and interactions of solitary waves in a 2 1 dimensional coupled nonlinear extension of the reaction diffusion equation the complete integrability of a 2 1 dimensional coupled nonlinear extension of the reaction diffusion cnlerd equation using the technique of painlev p analysis is investigated using the formalism of weiss et al 1983 j math phys 24 522 the arbitrariness of the expansion coefficients are proved besides following the hirota s formalism hirota r 1980 direct methods in soliton theory soliton berlin springer combined to weiss et al s methodology weiss et al 1984 j math phys 25 13 the consistency of the truncation is shown thus without the use of kruskal s simplification the bcklund transformation bt of the equations is obtained via the truncation procedure taking into account the arbitrariness of the expansion coefficients in the foregoing truncation a typical spectrum of localized coherent structures may be unearthed the scattering behavior of such structures is also investigated

on the integrability of systems of nonlinear ordinary differential equations with superposition principles a new class of solvable nonlinear dynamical systems has been recently identified by the requirement that the ordinary differential equations ode s describing each member of this class possess nonlinear superposition principles these systems of ode s are generally not derived from a hamiltonian and are classified by associated pairs of lie algebras of vector fields in this paper all such systems of n 3 ode s are integrated in a unified way by finding explicit integrals for them and relating them all to a pivotal member of their class the projective riccati equations moreover by perturbing two parametrically driven projective riccati equations thus making them nonsolvable in the above sense evidence is discovered of chaotic behavior on the poincare surface of section in the form of sensitive dependence on initial conditions near a boundary separating bounded from unbounded motion

distinguishability of discrete time nonlinear systems this note considers the problem of identifying a discrete time nonlinear system within a finite family of possible models from data sequences of a finite length the problem is approached by resorting to the notion of output distinguishability this amounts to asking whether output data sequences generated by different models can be distinguished from one another a number of results are presented with examples connections with conditions for linear systems are established

kowalewski s asymptotic method kac moody lie algebras and regularization we use an effective criterion based on the asymptotic analysis of a class of hamiltonian equations to determine whether they are linearizable on an abelian variety i e solvable by quadrature the criterion is applied to a system with hamiltonian h 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 sum limits i 1 l p i 2 sum limits i 1 l 1 exp left sum limits j 1 l n ij x j right parametrized by a real matrixn n ij of full rank it will be solvable by quadrature if and only if for alli j 2 n nt ij n n t jj 1 is a nonpositive integer i e the interactions correspond to the toda systems for the kac moody lie algebras the criterion is also applied to a system of gross neveu

indiscernible topological variations in dae networks a problem of characterizing conditions under which a topological change in a network of differential algebraic equations daes can go undetected is considered it is shown that initial conditions for which topological changes are indiscernible belong to a generalized eigenspace shared by the nominal system and the system resulting from a topological change a condition in terms of eigenvectors of the nominal system is derived to check for existence of possibly indiscernible topological changes for homogeneous networks this condition simplifies to the existence of an eigenvector of the laplacian of network having equal components lastly a rank condition is derived which can be used to check if a topological change preserves regularity of the nominal network

new exact solutions for the 2 1 dimensional generalized broer kaup system abstract the 1 1 dimensional broer kaup system which describes the propagation of shallow water waves is extended to a generalized 2 1 dimensional model with painleve property in this paper based on the general variable separation approach and two extended riccati equations we first find several new families of exact soliton like solutions and periodic like wave solutions with arbitrary functions for the 2 1 dimensional simplified generalized broer kaup gbk system b 0 abundant new localized excitations can be found by selecting appropriate functions after that we consider the conditions of b 0 to the gbk and several new results are obtained

bifurcation studies on travelling wave solutions for nonlinear intensity klein gordon equation abstract in this paper we study the travelling waves for the n 1 dimensional klein gordon equation with nonlinear intensity by using the bifurcation theory and methods of planar dynamic systems with the aid of maple we obtain all bifurcations and phase portraits in the parametric space moreover we explain the reason for appearance of nonsmooth travelling waves and for persistence of smoothness of smooth travelling waves and show the existence of smooth and nonsmooth solitary and periodic waves under different regions of parametric space various sufficient conditions to guarantee the existence of the above solutions are given

travelling wave solutions in the generalized hirota satsuma coupled kdv system by using the bifurcation theory of dynamical systems to the generalized hirota satsuma coupled kdv system bifurcation parameter sets are shown numbers of solitary waves kink waves and periodic waves are given under various parameter conditions all explicit formulas of solitary wave solutions and kink wave solutions and periodic wave solutions are listed

solitary wave solutions for a generalized hirota satsuma coupled kdv equation the solitary wave solutions of a generalized hirota satsuma coupled kdv equation are obtained exactly by using the decomposition method the solutions were calculated in the form of a convergent power series with easily computable components a variety of initial value system is considered the convergence of the method as applied to the coupled kdv equation is illustrated numerically the present algorithm performs extremely well in terms of accuracy and simplicity

a analytic and numerical solution to a modified kawahara equation and a convergence analysis of the method abstract in this paper we present an adomian s decomposition method shortly adm for numerical approximation traveling wave solutions of the modified kawahara equation the numerical solutions are compared with the known analytical solutions we also prove the convergence of adomian decomposition method adm applied to the modified kawahara equation

on mode reconstructability and reconstructability sets of piecewise linear systems this paper focuses on the problem of mode reconstructability of piecewise linear multi output systems for the case when a partition of the state space characterises the switching modes the partiti

soliton solutions and doubly periodic wave solutions for a new generalized hirota satsuma coupled system in this paper a new algebraic method with symbolic computation is presented to uniformly construct a series of exact solutions for general nonlinear equations compared with most existing tanh methods the proposed method not only gives new and more general solutions but also provides a guideline to classify the various types of the solutions according to the values of some parameters for illustration we apply the proposed method to solve a new generalized hirota satsuma coupled system and explicitly construct a series of exact solutions which include the soliton solutions and elliptic doubly periodic solutions as special cases in addition the links among our proposed method the tanh method and the extended method are also clarified generally

on location observability notions for switching systems abstract the focus of this paper is on the analysis of initial discrete state distinguishability notions for switching systems in a discrete time setting moreover the relationship between initial discrete state distinguishability and the problem of reconstructing the current discrete state is addressed

mode observability degree in discrete time switching linear systems abstract in this paper we consider the problem of identifying the active mode of a switching linear system from data sequences of a finite length the results combine elements from canonical correlation analysis and subspace projection methods in addition to providing insight into the geometric meaning of the problem the results turn out to be of practical relevance whenever mode identification is addressed in the presence of noisy corrupted measurements in particular the results can be used to provide conditions under which mode identification occurs independently of a prescribed noise level

a numerical solution of the coupled sine gordon equation using the modified decomposition method the modified decomposition method has been implemented for solving a coupled sine gordon equation we consider a system of coupled sine gordon equation which models one dimensional nonlinear wave processes in two component media by using an initial value system the numerical solutions of coupled sine gordon equation have been represented graphically

new exact jacobi elliptic functions solutions for the generalized coupled hirota satsuma kdv system abstract in this paper an generalized jacobi elliptic functions expansion method with computerized symbolic computation is used for constructing more new exact jacobi elliptic functions solutions of the generalized coupled hirota satsuma kdv system as a result eight families of new doubly periodic solutions are obtained by using this method some of these solutions are degenerated to solitary wave solutions and triangular functions solutions in the limit cases when the modulus of the jacobi elliptic functions m 1 or 0 which shows that the applied method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics

bifurcation method and traveling wave solution to whitham broer kaup equation by using bifurcation method to whitham broer kaup shallow water equations bifurcation parameter sets are shown numbers of solitary waves kink waves and periodic waves are given under various parameter conditions all explicit formulas of solitary wave solutions kink wave solutions and periodic wave solutions are listed

subspace angles between arma models abstract we define a notion of subspace angles between two linear autoregressive moving average single input single output models by considering the principal angles between subspaces that are derived from these models we show how a recently defined metric for these models which is based on their cepstra relates to the subspace angles between the models

applications of the combined tanh function method with symmetry method to the nonlinear evolution equations based on the symbolic computation we combined the tanh function method with the symmetry method to construct new type of solutions of the nonlinear evolution equations for the first time with the combined method some new types of solutions of the coupled 2 1 dimensional nonlinear system of schrodinger equations were obtained and their properties were studied by analyzing their figures

a decomposition method for finding solitary and periodic solutions for a coupled higher dimensional burgers equations in this paper we consider coupled higher dimensional burgers chdbur equations we find periodic solutions to chdbur equations using a modified adomian s decomposition method madm we find both exact and numerical solutions we compared the numerical solutions with corresponding analytical solutions we also show the effectiveness of the method

note on exact solutions for a class of nonlinear diffusion equations an effective characterization is given for a class of generalized nonlinear diffusion equations with power law dependent terms further a new auxiliary equation ansatz is derived consequently new exact traveling wave trigonometric function solitary like and weierstrass elliptic solutions to a subclass are obtained by means of an auxiliary equation method and a generalized riccati equation expansion method

a numerical simulation and explicit solutions of the generalized burgers fisher equation we consider solitary wave solutions of the generalized burgers fisher bf equation u t pu ru x u x x qu 1 u r 0 in this paper by considering the decomposition scheme we first obtain the exact solutions of the generalized bf equation for the initial condition without using any classical transformations and then its numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions its remarkable accuracy is finally demonstrated in the study of some values r 2 of the generalized bf equation

exact and numerical traveling wave solutions for nonlinear coupled equations using symbolic computation we find the explicit and numerical traveling wave solutions for a coupled kdv equation and a coupled mkdv equation by using the decomposition method with help of symbolic computation by using this method the solutions were calculated in the form of a convergent power series with easily computable components the convergence of the method as applied to the coupled kdv and mkdv equations is illustrated numerically

exact travelling wave solutions of nonlinear evolution equations in 1 1 and 2 1 dimensions abstract based upon the symbolic computation system maple the projective riccati equation method is improved to seek for travelling wave solutions in 1 1 and 2 1 dimensional nonlinear evolution equations by introducing two new elementary bell shaped and kink shaped functions the validity and reliability of the method is tested by applying it to the 2 1 dimensional generalized of the shallow water wave equation potential kdv equation and burgers kdv equation

a new method for a generalized hirota satsuma coupled kdv equation abstract in this paper differential transform method dtm which is one of the approximate methods is implemented for solving the nonlinear hirota satsuma coupled kdv partial differential equation a variety of initial value system is considered and the convergence of the method as applied to the hirota satsuma coupled kdv equation is illustrated numerically the obtained results are presented and only few terms of the expansion are required to obtain the approximate solution which is found to be accurate and efficient numerical examples are illustrated the pertinent features of the proposed algorithm

algebraic solution of the lindblad equation for a collection of multilevel systems coupled to independent environments we consider the lindblad equation for a collection of multilevel systems coupled to independent environments the equation is symmetric under the exchange of the labels associated with each system and thus the open system dynamics takes place in the permutation symmetric subspace of the operator space the dimension of this space grows polynomially with the number of systems we construct a basis of this space and a set of superoperators whose action on this basis is easily specified for a given number of levels m these superoperators are written in terms of a bosonic realization of the generators of the lie algebra in some cases these results enable finding an analytic solution of the master equation using known lie algebraic methods to demonstrate this we obtain an analytic expression for the state operator of a collection of three level atoms coupled to independent radiation baths when analytic solutions are difficult to find the basis and the superoperators can be used to considerably reduce the computational resources required for simulations

a direct algebraic approach to observer design under switching measurement equations based on the algebraic transformation of a switched linear measurement equation into a nonlinear yet deterministic equation an asymptotic state observer is constructed for discrete time linear systems whose observations are generated according to randomly switching measurement modes the observer which combines the algebraic transformation with a newton observer applied to the resulting nonlinear measurement equation is shown to be locally exponentially convergent under arbitrary mode sequences

on classes of integrable systems and the painleve property the caudrey dodd gibbon equation is found to possess the painleve property investigation of the backlund transformations for this equation obtains the kuperschmidt equation a certain transformation between the kuperschmidt and caudrey dodd gibbon equation is obtained this transformation is employed to define a class of p d e s that identically possesses the painleve property for equations within this class backlund transformations and rational solutions are investigated in particular the sequences of higher order kdv caudrey dobb gibbon and kuperschmidt equations are shown to possess the painleve property

lie group method for solving generalized hirota satsuma coupled korteweg de vries kdv equations method of lie group has been applied to study hirota satsuma coupled korteweg de vries kdv system of partial differential equations lie group method is applied to determine symmetry reductions of the nonlinear partial differential equations the resulting nonlinear ordinary differential equations are solved analytically and the obtained solutions are presented graphically

the homotopy types of the posets of p subgroups of a finite group abstract we study the homotopy properties of the posets of p subgroups s p g and a p g of a finite group g viewed as finite topological spaces we answer a question raised by r e stong in 1984 about the relationship between the contractibility of the finite space a p g and that of s p g negatively and describe the contractibility of a p g in terms of algebraic properties of the group g

model based modes detection and discernibility for switched affine discrete time systems this paper addresses the problem of modes detection for switching discrete time linear and affine systems a unified presentation of the model based methods with the corresponding modes detectors is carried out and a comparative study is conducted next the different notions of discernibility proposed in the literature are presented such notions are central since they guarantee the uniqueness of the solution delivered by the modes detectors a complete step by step procedure of modes detection is proposed the paper includes whenever necessary some extensions of the existing results

an application of the decompositionmethod for the two dimensional kdv burgers equation a relatively new decomposition method is presented to find the explicit and numerical solutions of the two dimensional korteweg de vries burgers equation tdkdvb for short for the initial conditions some numerical results are also given for this equation by using the decomposition method

on the complete and partial integrability of non hamiltonian systems abstract the methods of singularity analysis are applied to several third order non hamiltonian systems of physical significance including the lotka volterra equations the three wave interaction and the rikitake dynamo model complete integrability is defined and new completely integrable systems are discovered by means of the painleve property in all these cases we obtain integrals which reduce the equations either to a final quadrature or to an irreducible second order ordinary differential equation ode solved by painleve transcendents relaxing the painleve property we find many partially integrable cases whose movable singularities are poles at leading order with in t t 0 terms entering at higher orders in an n th order generalized rossler model a precise relation is established between the partial fulfillment of the painleve conditions and the existence of n 2 integrals of the motion

a stronger reformulation of webb s conjecture in terms of finite topological spaces abstract we investigate a stronger formulation of webb s conjecture on the contractibility of the orbit space of the p subgroup complexes in terms of finite topological spaces the original conjecture which was first proved by symonds and more recently by bux libman and linckelmann can be restated in terms of the topology of certain finite spaces we propose a stronger conjecture and prove various particular cases by combining fusion theory of finite groups and homotopy theory of finite spaces

a symbolic computational method for constructing exact solutions to difference differential equations in this paper we extended tanh method to solve difference differential equations and pure difference equations with the projective riccati equation as an example we applied this method to a 2 1 dimensional toda lattice equation as a result many exact solutions are obtained with the help of symbolic system maple including soliton solutions presented by hyperbolic functions sinh and cosh periodic solutions presented by sin and cos and rational solutions this method can also be used to other nonlinear difference differential equations

a functional realization of 3 ℝ providing minimal vessiot guldberg lie algebras of nonlinear second order ordinary differential equations as proper subalgebras a functional realization of the lie algebra sl3 r as a vessiot guldberg lie algebra of second order differential equation sode lie systems is proposed it is shown that a minimal vessiot guldberg lie algebra lvg is obtained from proper subalgebras of sl3 r for each of the sode lie systems of this type by particularization of one functional and two scalar parameters of the sl3 r realization the relation between the various vessiot guldberg lie algebras by means of a limiting process in the scalar parameters further allows to define a notion of contraction of sode lie systems

on the numerical solution of the system of two dimensional burgers equations by the decomposition method adomian s decomposition method adm is proposed to approximate the numerical and analytical solutions of system two dimensional burgers equations stdbe with initial conditions the advantages of this work are the decomposition method reduces the computational work and improvement with regard to its accuracy and rapid convergence some examples are given to illustrate the performance of the method described

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

new exact travelling wave solutions for the shallow long wave approximate equations based upon a generally projective riccati equation method which is a direct and unified algebraic method for constructing more general form travelling wave solutions of nonlinear partial differential equations and implemented in a computer algebraic system we consider the shallow long wave approximate equations new and more general form solutions are obtained including kink shaped solitons bell shaped solitons singular solitons and periodic solutions the properties of the new formal solitary wave solutions are shown by some figures

a reliable modification of adomian decomposition method in this paper we propose a powerful modification of adomian decomposition method that will accelerate the rapid convergence of the series solution the validity of the modified technique is verified through illustrative examples in all cases of differential and integral equations we obtained excellent performance from the modified algorithm the modification could lead to a promising approach for many applications in applied sciences

bifurcations of traveling wave solutions for a class of the generalized benjamin bona mahony equation abstract by using the theory of bifurcations of dynamical systems to a class of the generalized benjamin bona mahony gbbm equation the existence of solitary wave solutions and uncountably infinite many smooth and non smooth periodic wave solutions are obtained it can be shown that the existence of singular curves in a traveling wave system is the reason why smooth waves converge to cusp waves finally when parameters are varied under different parametric conditions various sufficient conditions to guarantee the existence of the above solutions are given

a numerical solution and an exact explicit solution of the nls equation we consider traveling wave solutions of the nonlinear schrodinger nls for short equation in this paper by considering the decomposition scheme we first obtain the exact solutions of the nls equation for the initial condition without using any classical transformations and then its numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions its remarkable accuracy is finally demonstrated in the study of some initial values of the nls equation

smooth and non smooth travelling wave solutions of generalized degasperis procesi equation abstract the dynamical behavior and special exact solutions of the generalized degasperis procesi equation u t c 0 u x u txx auu x 3 u x u xx uu xxx is analyzed by using bifurcation theory and the method of phase portraits analysis as a result the analytic expressions of peakon solutions compacton solutions and periodic cusp wave solutions are obtained and the condition under which peakon and compacton solutions appear are also given in the meantime the reason that solitary cusp wave and periodic cusp wave appear is given

symbolic computation and a uniform direct ansatze method for constructing travelling wave solutions of nonlinear evolution equations on the basis of the computer symbolic system maple and the tanh method the riccati equation method as well as all kinds of improved versions of these methods we present a further uniform direct ansatze method for constructing travelling wave solutions of nonlinear evolution equations compared with the existing methods the presented method can be used to construct more new general solutions and we give some examples to illustrate the key step of our method

on the use of isospectral eigenvalue problems for obtaining hereditary symmetries for hamiltonian systems we present an algorithmic method for obtaining an hereditary symmetry the generalized squared eigenfunction operator from a given isospectral eigenvalue problem this method is applied to the n n eigenvalue problem considered by ablowitz and haberman and to the eigenvalue problem considered by alonso the relevant hamiltonian formulations are also determined finally an alternative method is presented in the case two evolution equations are related by a miura type transformation and their hamiltonian formulations are known

a new riccati equation expansion method with symbolic computation to construct new travelling wave solution of nonlinear differential equations abstract in this paper based on a new system of riccati equations we present a triple riccati equation expansion method the nonlinear klein gordon equation and the combined kdv mkdv equation are chosen to illustrate the method as a result many new travelling solutions which include bell profile solitary wave solution singular solitary solutions periodic solutions are obtained this method can be used to the other nonlinear evolution equations in mathematics physics

sine gordon and modified korteweg de vries charges the sine gordon and the integrated modified korteweg de vries equations are shown to conserve the same infinite set of charges the charges are determined by a recursion relation as a consequence the solutions of all the equations generated by the charges have in common all time independent properties

exact and numerical traveling wave solutions of whitham broer kaup equations in this paper we find the explicit and numerical traveling wave solutions of whitham broer kaup for short wbk equations which contain blow up solutions and periodic solutions by using the decomposition method by using this method the solutions were calculated in the form of a convergent power series with easily computable components the convergence of the method as applied to the whitham broer kaup equations is illustrated numerically

some new integrable nonlinear evolution equations and darboux transformation two classes of new nonlinear evolution equations are derived with the aid of a 4 4 matrix spectral problem with three potentials a darboux transformation for the first nontrivial nonlinear evolution equation is given based on the gauge transformation between the corresponding 4 4 matrix spectral problems as an application of the darboux transformation some explicit solutions of the nontrivially nonlinear evolution equation are obtained

superposition formulas for pseudounitary matrix riccati equations the purpose of this article is to derive a superposition formula for the pseudounitary matrix riccati equation of dimension n 2 the superposition formula will be written in closed form in terms of five particular solutions satisfying certain well specified conditions defining a fundamental set examples will be studied in order to show how the superposition formula works and how it can be used in numerical calculations

exact solutions of a hierarchy of mixing speeds models this paper presents several new aspects of discrete kinetic theory dkt first a hierarchy of d dimensional d 1 2 3 models is proposed with 2d 3 velocities and three moduli speeds 0 2 and a third one that can be arbitrary it is assumed that the particles at rest have an internal energy which for microscopic collisions supplies for the loss of the kinetic energy in a more general way than usual collisions are allowed that mix particles with different speeds second for the 1 1 dimensional restriction of the systems of pde for these models which have two independent quadratic collision terms we construct different exact solutions the usual types of exact solutions are studied periodic solutions and shock wave solutions obtained from the standard linearization of the scalar riccati equations called riccatian shock waves then other types of solutions of the coupled riccati equations are found called non riccatian shock waves and they are compared with the previous ones the main new result