New Exact Solutions to （2＋1）-Dimensional Dispersive Long Wave Equations

Based upon a further extended tanh method [Phys. Lett. A307 (2003) 269; Chaos, Solitons and Fractals 17 (2003) 669] and the symbolic computation system, Maple, we consider the (2 1)-dimensional dispersive long waveequations. We obtain many new solutions of the equation. These solutions contain solitomlike solutions, periodic form solutions, and some rational solutions.     

(2+1)-维色散长波方程的折叠孤立波解

本文利用一种该进的映射法和线性变量分离法,得到（2+1）-维色散长波方程大量的,带有两个任意函数的精确解。并在得到的一个周期波精确解的基础上,通过选择恰当的函数,可以观察到（2+1）-维色散长波方程的折叠孤立波的演化行为。     

New Exact Travelling Wave Solutions to Hirota Equation and (1+1)-Dimensional Dispersive Long Wave Equation

Based on the computerized symbolic Maple, we study two important nonlinear evolution equations, i.e.,the Hirota equation and the (1+1)-dimensional dispersive long wave equation by use of a direct and unified algebraic method named the general projective Riccati equation method to find more exact solutions to nonlinear differential equations. The method is more powerful than most of the existing tanh method. New and more general form solutions are obtained. The properties of the new formal solitary wave solutions are shown by some figures.     

New Exact Solutions to Dispersive Long-Wave Equations in (2+1)-Dimensional Space

New exact solutions expressed by the Jacobi elliptic functions are obtained to the (2+1)-dimensional dispersive long-wave equations by using the modified F-expansion method. In the limit case, new solitary wave solutions and triangular periodic wave solutions are obtained as well.     

New Families of Rational Form Variable Separation Solutions to （2＋1）-Dimensional Dispersive Long Wave Equations

With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the （2＋1）-dimensional dispersive long wave equations are constructed by means of a function transformation, improved mapping approach, and variable separation approach, among which there are rational solitary wave solutions, periodic wave solutions and rational wave solutions.     

New Complexiton Solutions of (1+1)-Dimensional Dispersive Long Wave Equation

By means of two different Riccati equations with different parameters as subequation in the components of finite rational expansion method, new complexiton solutions for the (1+1)-dimensional dispersive long wave equation are successfully constructed, which include various combination of trigonometric periodic and hyperbolic function solutions, various combination of trigonometric periodic and rational function solutions, and various combination of hyperbolic and rational function solutions.     

Symmetry Groups and New Exact Solutions of （2＋1）-Dimensional Dispersive Long-Wave Equations

Using the modified CK＇s direct method, we derive a symmetry group theorem of （2＋1）-dimensional dispersive long-wave equations. Based upon the theorem, Lie point symmetry groups and new exact solutions of （2＋1）- dimensional dispersive long-wave equations are obtained.     

Periodic Wave Solutions to Dispersive Long-Wave Equations in (2+1)-Dimensional Space

Periodic wave solutions to the dispersive long-wave equations are obtained by using the F-expansion method, which can be thought of as a generalization of the Jacobi elliptic function method. In the limit case, solitary wave solutions are obtained as well.     

Periodic Wave Solutions to Dispersive Long-Wave Equations in （2＋1）-Dimensional Space

Periodic wave solutions to the dispersive long-wave equations are obtained by using the F-expansion method, which can be thought of as a generalization of the Jacobi elliptic function method. In the limit case, solitary wave solutions are obtained as well.     

New Exact Solutions to (2+1)-Dimensional Variable Coefficients Broer-Kaup Equations

In this paper, using the variable coefficient generalized projected Ricatti equation expansion method, we present explicit solutions of the (2 1)-dimensional variable coefficients Broer-Kaup (VCBK) equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions.Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.     

New Exact Solutions to （2＋1）-Dimensional Variable Coefficients Broer-Kaup Equations

In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the （2＋1）-dimensional variable coefficients Broer-Kaup （VCBK） equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.     

Rational Form Solitary Wave Solutions and Doubly Periodic Wave Solutions to(1+1)-Dimensional Dispersive Long Wave Equation

In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.     

Bäcklund Transformat ion and Mult isoliton-Like Solutions for (2+1)-Dimensional Dispersive Long Wave Equations

A Bäcklund transformation of the (2+1)-dimensional dispersive long wave equations is derived by using the developed homogeneous balance method. by means of the Bäcklund transformation, the new multisoliton-like solution and other two types of exact solutions to these equations are constructed.     

Some New Exact Solutions to the Dispersive Long-Wave Equation in(2+1)-Dimensional Spaces

In this paper, by using a further extended tanh method and symbolic computation system, some newsoliton-like and period form solutions of the dispersive long-wave equation in (2 1)-dimensional spaces are obtained.     

Some New Exact Solutions to the Dispersive Long－Wave Equation in（2＋1）－Dimensional Spaces

In this paper, by using a further extended tanh method- and symbolic computation system, some new soliton-like and period form solutions of the dispersive long-wave equation in (2 l )-dimensional spaces are obtained.     

Multiple Soliton-Like Solutions for (2 + 1)-Dimensional Dispersive Long-Wave Equations

By using a homogeneous balance method,multiple-solitonlike solutions of the (2 +1)-dimensional dispersive long-wave equation areconstructed. The method used here can be generalized toa wide class of nonlinear evolution equations.     

New Exact Solutions of the Integrable Broer-Kaup Equations in (2+1)-Dimensional Spaces

In this paper, by improving some procedure of extended tanh-function method, some new exact solutions to the integrable Broer-Kaup equations in (2+1)-dimensional spaces are obtained, which include soliton-like solutions, solitary wave solutions, trigonometric function solutions, and rational solutions.     

New Families of Nontravelling Wave Solutions to Two (3+1)-Dimensional Equations

In this paper, two (3+1)-dimensional equations are investigated. Auto-Bäcklund transformation is obtained, which is used with some ansatze to seek new types of exact solutions including some arbitrary functions. When these arbitrary functions are taken as some special functions, these solutions possess abundant structures. These solutions contain soliton-like solutions and rational solutions.