Exact solutions for the coupled Klein-Gordon-Schrǒdinger equations using the extended F-expansion method

The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.     

New Exact Solutions to Long-Short Wave Interaction Equations

New exact solutions expressed by the Jacobi elliptic functions are obtained to the long-short wave interaction equations by using the modified F-expansion method. In the limit case, solitary wave solutions and triangular periodic wave solutions are obtained as well.     

修正Jacobi椭圆函数展开法及其应用

对Jacobi椭圆函数展开法进行了扩展, 且应用修正过的方法获得了若干非线性波动方程的更多的准确周期解, 补充了前面研究所得的结果.关键词：Jacobi椭圆函数展开法非线性演化方程精确解周期解     

广义Boussinesq方程的无穷序列新精确解

以辅助方程法为基础,给出第二种椭圆方程解的非线性叠加公式,借助符号计算系统Mathematica获得了广义Boussinesq方程的无穷序列新精确解.这里包括无穷序列Jacobi椭圆函数精确解、无穷序列孤立波解和无穷序列三角函数解.该方法在构造非线性发展方程无穷序列精确解方面具有普遍意义.     

A Generalization of F-Expansion Method and Its Application to （2＋l）-Dimensional Boussinesq Equation

A new generalized F-expansion method is introduced and applied to the study of the （2＋1）-dimensional Boussinesq equation. The further extension of the method is discussed at the end of this paper.     

非线性Schrodinger方程的Jacobi椭圆函数包络解

通过函数变换和扩展Jacobi椭圆函数展开法,利用吴消元法,借助符号运算软件Maple,得到非线性Schringer方程丰富的包络形式精确解,特别是由两个Jacobi椭圆函数表示的精确解.当模数m→1或m→0时,一部分解退化为双曲函数或三角函数表示的解,F-展开法和扩展的F-展开法得到的精确解是本文结果的特例.     

New Extended Jacobi Elliptic Function Rational Expansion Method and Its Application

In this paper, an extended Jacobi elliptic function rational expansion method is proposed for constructing new forms of exact Jacobi elliptic function solutions to nonlinear partial differential equations by means of making a more general transformation. For illustration, we apply the method to the (2 1)-dimensional dispersive long wave equation and successfully obtain many new doubly periodic solutions, which degenerate as soliton solutions when the modulus m approximates 1. The method can also be applied to other nonlinear partial differential equations.     

The Peridic Wave Solutions for Two Nonlinear Evolution Equations

By using the F-expansion method proposed recently, the periodic wave solutions expressed by Jacobielliptic functions for two nonlinear evolution equations are derived. In the limit cases, the solitary wave solutions andthe other type of traveling wave solutions for the system are obtained.     

Multiple Jacobi Elliptic Function Solutions to Integrable Higher Order Broer-Kaup Equation in (2+1)-Dimensional Spaces

In this paper, we improve the method for deriving Jacobi elliptic function solutions of nonlinear evolution equations given in Ref. [12] and apply it to the integrable higher-order Broer-Kaup system in (2 1)-dimensional spaces.Some new elliptic function solutions are obtained.     

Multiple Jacobi Elliptic Function Solutions to Integrable Higher Order Broer-Kaup Equation in （2＋1）-Dimensional Spaces

In this paper, we improve the method for deriving Jacobi elliptic function solutions of nonlinear evolution equations given in Ref. [12] and apply it to the integrable higher-order Broer-Kaup system in （2＋1）-dimensional spaces. Some new elliptic function＂ solutions are obtained.     

A Generalized F-expansion Method and Its Application in High-Dimensional Nonlinear Evolution Equation

A generalized F-expansion method is introduced and applied to (3 1)-dimensional Kadomstev-Petviashvili(KP) equation. As a result, some new Jacobi elliptic function solutions of the equation are found, from which the trigonometric function solutions and the solitary wave solutions can be obtained. The method can also be extended to other types of nonlinear evolution equations in mathematical physics.     

Abundant Multisoliton Structure of (3+1)-Dimensional Breaking Soliton Equation

Using the extended homogeneous balance method, we obtained abundant exact solution structures of the (3 1 )-dimensional breaking soliton equation. By means of the leading order term analysis, the nonlinear transformations of the (3t1)-dimensional breaking soliton equation are given first, and then some special types of single solitary wave solutions and the multisoliton solutions are constructed.