explicit series solutions to nonlinear evolution equations the sine cosine method in this paper a sine cosine method is used to construct many periodic and solitary wave solutions to two nonlinear evolution systems the coupled quadratic nonlinear equations and the coupled klein gordon schrodinger equations under different parameter conditions explicit formulas for some new periodic and solitary wave solutions are successfully obtained the proposed solutions are found to be important for the explanation of some practical physical problems

new periodic and soliton solutions by application of exp function method for nonlinear evolution equations in this letter the kaup kupershmidt 2 1 dimensional potential kadomtsev petviashvili shortly pkp equations are presented and the exp function method is employed to compute an approximation to the solution of nonlinear differential equations governing the problem it has been attempted to show the capabilities and wide range applications of the exp function method this method can be used as an alternative to obtain analytic and approximate solution of different types of differential equations applied in engineering mathematics

abundant new exact solutions for the 3 1 dimensional jimbo miwa equation in this paper by using the generalized riccati equation mapping method and picking up its new solutions authors obtain abundant new exact solutions including kink solutions periodic form solutions soliton like solutions and rational solutions to a 3 1 dimensional jimbo miwa equation respectively

some new periodic solitary wave solutions of 3 1 dimensional generalized shallow water wave equation by lie symmetry approach abstract many important physical situations such as fluid flows marine environment solid state physics and plasma physics have been represented by shallow water wave equations in this article we construct new solitary wave solutions for the 3 1 dimensional generalized shallow water wave gsww equation by using optimal system of lie symmetry vectors the governing equation admits twelve lie dimension space a variety of analytic closed form solutions such as new periodic solitary wave cross kink soliton and doubly periodic breather type solutions have been obtained by using invariance of the concerned 3 1 dimensional gsww equation under one parameter lie group of transformations lie symmetry transformations have applied to generate the different forms of invariant solutions of the 3 1 dimensional gsww equation for different lie algebra lie symmetry method reduces 3 1 dimensional gsww equation into various ordinary differential equations odes while one of the lie algebra it is transformed into the well known 2 1 dimensional blmp equation it is affirmed that the proposed techniques are convenient genuine and powerful tools to find the exact solutions of nonlinear partial differential equations pdes under the suitable choices of arbitrary functions and parameters 2d 3d and contour graphics to the obtained results of gsww equation are also analyzed

symmetry analysis of the infeld rowlands equation a fourth order nonlinear evolution equation in 2 1 dimensions arising in the study of soliton stability is analyzed its symmetry group is shown to be infinite dimensional and is used to obtain particular solutions the equation is shown not to have the painlev e property

a generalized weierstrass elliptic function expansion method for solving some nonlinear partial differential equations the present paper deals with families of non trivial solutions of the equation email protected 2 pw 4 x qw 2 x r on the basis of these solutions a direct and generalized algebraic algorithm is described for constructing the new solutions of some nonlinear partial differential equations nlpdes subsequently many new and more general exact solutions in terms of the weierstrass elliptic function x g 2 g 3 are obtained the method can be applied to other nlpdes in mathematical physics

generalized riccati equation expansion method and its application to the 3 1 dimensional jumbo miwa equation based on the computerized symbolic system maple and a riccati equation a generalized riccati equation expansion method for constructing soliton like solutions of non linear evolution equations nees is presented by a new general ansatz the proposed method is more powerful than most of the existing tanh methods the extended tanh function method the modified extended tanh function method and generalized hyperbolic function method by use of the method we not only can successfully recover the previously known formal solutions but also construct new and more general formal solutions for some nees making use of the method we study the the 3 1 dimensional jumbo miwa equation and obtain rich new families of the exact solutions including the non travelling wave and coefficient functions soliton like solutions singular soliton like solutions periodic form solutions

convergence of mayer expansions the tree graph bound of battle and federbush is extended and used to provide a simple criterion for the convergence of iterated mayer expansions as an application estimates on the radius of convergence of the mayer expansion for the two dimensional yukawa gas nonstable interaction are obtained

explicit periodic solitary wave solutions for the 2 1 dimensional boussinesq equation in this paper 2 1 dimensional boussinesq equation is investigated by using homoclinic test method with the aid of maple new explicit periodic solitary wave solutions are obtained moreover mechanical feature of wave is exhibited

on the extended applications of homogenous balance method in this paper we study the travelling wave reductions for certain 2 1 and 3 1 dimensional physically important nonlinear evolutionary equations by using the recently proposed homogenous balance method hbm through this analysis we explore certain new solutions for the equations we have studied

iterated mayer expansion for classical gases at low temperatures we derive iterated mayer expansions for classical gases and establish recursive bounds which control their convergence these bounds are useful for gases with two body forces which are strong and possibly attractive at distances that are short compared to their range our procedure is based on splitting the potential into pieces of decreasing strength and increasing range this may be called a renormalization group treatment of a classical gas we apply our results to yukawa lattice gas models and obtain convergence of series expansions for the pressure for a range of parameters temperature fugacities range of the interaction that was inaccessible before application to 3 dimensionalu 1 lattice gauge theory coulomb gas z ferromagnet will be made elsewhere

comment on on the extended applications of homogeneous balance method in this letter we show that all results presented in senthilvelan s paper can be actually obtained by a direct method

new soliton like solutions to the potential kadomstev petviashvili pkp equation in this paper new soliton like solutions are obtained for 2 1 dimensional potential kadomstev petviashvili pkp equation by using the symbolic computation method developed by gao and tian solitary wave solutions obtained in appl math comput 123 2001 29 are merely a special case in this paper the method can also be extended to other types of nolionear evolution equations in mathematical physics

applications of a further extended tanh method by using a further extended tanh method chaos solitons fract 17 2003 669 and symbolic computation system maple we obtain abundant new explicit exact solutions of the 2 1 dimensional burgers equation and the 2 1 dimensional boussinesq equation the new solutions including soliton like solutions period form solutions and some other solutions

mayer expansions and the hamilton jacobi equation we review the derivation of wilson s differential equation in infinitely many variables which describes the infinitesimal change in an effective potential of a statistical mechanical model or quantum field theory when an infinitesimal integration out is performed we show that this equation can be solved for short times by a very elementary method when the initial data are bounded and analytic the resulting series solutions are generalizations of the mayer expansion in statistical mechanics the differential equation approach gives a remarkable identity for connected parts and precise estimates which include criteria for convergence of iterated mayer expansions applications include the yukawa gas in two dimensions past the 4 threshold and another derivation of some earlier results of gopfert and mack

are all the equations of the kadomtsev petviashvili hierarchy integrable the kadomtsev petviashvili kp hierarchy is an infinite set of nonlinear partial differential equations in which the number of independent variables increases indefinitely as one proceeds down the hierarchy since these equations were obtained as part of a group theoretical approach to soliton equations it would appear that the kp hierarchy provides integrable scalar equations with an arbitrary number of independent variables it is shown by investigating a specific equation in 3 1 dimensions that the higher equations in the kp hierarchy are only integrable in a conditional sense the equation under study taken in isolation does not pass certain well known and reliable integrability tests thus applying painleve analysis we find that solutions exist allowing movable critical points furthermore solitary wave solutions are shown to exist that do not behave like solitons in multiple collisions on the other hand if the dependence of a solution on the first 2 1 variables is restricted by the fact that it should also satisfy the kp equation itself then the integrability conditions in the other dimensions are satisfied conditional integrability thus means that linear techniques will provide only those solutions of equations in the hierarchy that simultaneously satisfy lower equations in the same hierarchy

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

symbolic computation and new families of exact travelling solutions for the kawahara and modified kawahara equations in this paper we consider the nonlinear evolution equations such as kawahara equation and modified kawahara equation by using the tanh method and an exp function method the travelling wave solutions for the these equations are presented new exact travelling solutions are explicitly obtained with the aid of symbolic computation the obtained solutions include compactons solitons solitary patterns and periodic solutions

new solitary wave solutions for two nonlinear evolution equations abstract in this paper multiple exp function method is employed to investigate exact multiple wave solutions for 2 1 dimensional potential kadomtsev petviashvili equation and 3 1 dimensional jimbo miwa equation not only already known multiple wave solutions are recovered but also several new or more general multiple wave solutions are obtained

an iterated mayer expansion for the yukawa gas we construct a convergent expansion for the yukawa gas at small activity and inverse temperature 4 e 2

exact solutions of coupled nonlinear klein gordon equation abstract in this paper we employ the general integral method for traveling wave solutions of coupled nonlinear klein gordon equations based on the idea of the exact jacobi elliptic function a simple and efficient method is proposed for obtaining exact solutions of nonlinear evolution equations the solutions obtained include solitons periodic solutions and jacobi elliptic function solutions

group theoretical analysis of dispersive long wave equations in two space dimensions abstract the symmetry algebra of an integrable dispersive long wave equation in two space dimensions is shown to be infinite dimensional and to have a kac moody virasoro structure the corresponding symmetry group is used to generate a large number of new solutions in particular solitons kinks and periodic waves these waves have wave crests of quite general shapes the results are compared to those for a nonintegrable two space dimensional dispersive long wave equation for which the symmetry group is finite dimensional and wave crests are always straight lines

a note on new travelling wave solutions to the ostrovsky equation in a recent paper by yasar e yasar new travelling wave solutions to the ostro vsky equation appl math comput 216 2010 3191 3194 new travelling wave solutions to the transformed reduced ostrovsky equation are presented in this note it is shown that some of these solutions are disguised versions of known solutions

boundary data smoothness for solutions of nonlocal boundary value problems for second order differential equations abstract under certain conditions solutions of the boundary value problem y f x y y y x 1 y 1 and y x 2 i 1 m r i y i y 2 are differentiated with respect to boundary conditions where a x 1 1 m x 2 b r 1 r m r and y 1 y 2 r

exact travelling wave solutions for a generalized zakharov kuznetsov equation in this paper by means of a proper transformation and symbolic computation we study the exact travelling wave solutions for a generalized zakharov kuznetsov gzk equation by using the extended tanh method and direct assumption method as a result rich exact travelling wave solutions which contain new kink shaped solitons bell shaped solitons periodic solutions combined formal solitons rational solutions and singular solitons for gzk equation are obtained

new exact solutions for some nonlinear differential equations using symbolic computation based on computerized symbolic computation and a new general ansatze a generalized tanh function method for constructing multiple travelling wave solutions of nonlinear evolution equations nees is presented and implemented in a computer algebraic system applying the generalized method with the aid of maple we consider some nees with physics interests as a result we can successfully recover the previously known solitary wave solutions that had been found by the extended tanh function method and other more sophisticated methods more importantly for some equations we also obtain other new and more general solutions at same time the results include kink profile solitary wave solutions bell profile solitary wave solutions periodic wave solutions rational solutions singular solutions and new formal solutions the properties of the new soliton solutions for wbk equations are shown by some figures

symbolic computation and various exact solutions of potential kadomstev petviashvili equation in this paper we make some improvement on the key steps of homogenous balance method and apply it to the research of potential kadomstev petviashvili equation various exact solutions include soliton multisoliton and rational type solutions of the equation are obtained

extend three wave method for the 1 2 dimensional ito equation abstract in this work extend three wave method etm is used to construct the novel multi wave solutions of the 1 2 dimensional ito equation as a result three soliton solution doubly periodic solitary wave solutions periodic two solitary wave solutions are obtained it is shown that the extend three wave method may provide us with a straightforward and effective mathematical tool for seeking multi wave solutions of higher dimensional nonlinear evolution equations

a note on abundant new exact solutions for the 3 1 dimensional jimbo miwa equation abstract we demonstrate that eight from twenty seven solutions obtained by li and dai abundant new exact solutions for the 3 1 dimensional jimbo miwa equation j math anal appl 361 2010 587 590 are wrong and do not satisfy the equation the other nineteen exact solutions are not new solutions and can be found from the well known solution

dynamical survey of a generalized zakharov equation and its exact travelling wave solutions we investigate the dynamical behavior of a generalized zakharov equation for the complex envelope of the high frequency wave and the real low frequency field by analyzing its phase portraits following a dynamical system approach in different parameter regions we depict phase portraits of a travelling wave system through discussing the bifurcation of phase portraits we unwrap explicit miscellaneous travelling waves including localized and periodic ones

symmetry reductions and new exact non traveling wave solutions of potential kadomtsev petviashvili equation with p power with the aid of maple symbolic computation and lie group method pkpp equation is reduced to some 1 1 dimensional partial differential equations in which there are linear pde with constant coefficients nonlinear pde with constant coefficients and nonlinear pde with variable coefficients using the separation of variables homoclinic test technique and auxiliary equation methods we obtain new abundant exact non traveling solutions with arbitrary functions for the pkpp

log sobolev inequality for the continuum sine gordon model we prove a multiscale generalisation of the bakry emery criterion for a measure to satisfy a log sobolev inequality our criterion relies on the control of an associated pde well known in renormalisation theory the polchinski equation it implies the usual bakry emery criterion but we show that it remains effective for measures which are far from log concave indeed using our criterion we prove that the massive continuum sine gordon model with beta 6 pi satisfies asymptotically optimal log sobolev inequalities for glauber and kawasaki dynamics these dynamics can be seen as singular spdes recently constructed via regularity structures but our results are independent of this theory

new exact solutions to the 2 1 dimensional ito equation extended homoclinic test technique exact soliton solutions to the 2 1 dimensional ito equation are studied based on the idea of extended homoclinic test and bilinear method some explicit solutions such as triangle function solutions soliton solutions doubly periodic wave solutions and periodic solitary wave solutions are obtained it shows that the 2 1 dimensional ito equation has richer solutions besides the elastic interactions of the solutions and their corresponding physical meaning are discussed

new solutions of the 3 1 dimensional jimbo miwa equation we find new exact solutions of the 3 1 dimensional jimbo miwa equation by applying the extended homogeneous balance method we also get an iterative formula of finding exact solutions this paper shows that there exist a lot of solutions for the 3 1 dimensional jimbo miwa equation

double periodic soliton solutions for the 3 1 dimensional boiti leon manna pempinelli equation in incompressible fluid abstract under investigation is the 3 1 dimensional boiti leon manna pempinelli equation in the incompressible fluid in this paper the extended homoclinic test technique ansatz functions and the bilinear form are used to construct double periodic soliton solutions of the 3 1 dimensional boiti leon manna pempinelli equation some entirely new double periodic soliton solutions are presented the properties and physical structure for these obtained solutions are discussed with some figures the ansatz functions are first used in 3 1 dimensional higher order differential equation

a variety of differentiability results for a multi point boundary value problem the goal of this work is to address differentiability of solutions of a nonlinear dynamic system with multi point boundary conditions described by x f t x m 1k mmx tm r where r rn and for each 1 m k mm is an n n constant matrix and tm t the solution of this system is defined on a measure chain t and x denotes a generalized derivative known as the delta derivative

the decomposition method for solving 2 1 dimensional boussinesq equation and 3 1 dimensional kp equation we study the solitary wave solutions of the 2 1 dimensional boussinesq equation u t t u x x u y y u 2 x x u x x x x 0 and 3 1 dimensional kp equation u x t 6u x 2 6uu x x u x x x x u y y u z z 0 in this paper by considering the decomposition scheme we first obtain the exact solitary wave solutions of the 2 1 dimensional boussinesq equation and 3 1 dimensional kp equation for the initial conditions 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 2 1 dimensional boussinesq equation and 3 1 dimensional kp equation