非线性波动方程的Jacobi椭圆函数包络周期解

应用Jacobi椭圆函数展开法求得了一类非线性波方程的包络周期解,而且用这种方法得到的周期解在一定条件下可以退化为包络冲击波解或包络孤立波解关键词：Jacobi椭圆函数 非线性方程 包络周期解 包络孤立波解     

长短波相互作用方程的Jacobi椭圆函数求解

推广了Jacobi椭圆函数展开方法,研究了复非线性演化方程组的求解问题,得到了长短波相互作用方程的准确包络周期解.该结果在一定条件下包含了相应的孤波解.关键词：Jacobi椭圆函数方法长短波相互作用方程孤波解     

Jacobi 椭圆函数展开法的新应用

通过引入“秩”的概念, 对非线性发展方程进行分类, 将Jacobi椭圆函数展开法推广应用到一类新的非线性发展方程, 并给出了它们的精确周期解.关键词：非线性发展方程周期解孤立波解Jacobi椭圆函数     

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     

弱色散非线性波动方程的孤波解和Jacobi椭圆函数解

应用影射法解传输线中弱色散非线性波动方程,得到了孤波解和Jacobi椭圆函数解,并用Matlab绘图加以说明.     

非线性波方程求解的新方法

从Legendre椭圆积分和Jacobi椭圆函数的定义出发,得到了新的变换,并把它用于非线性演化方程的求解.用三个具体的例子,如非线性Klein-Gordon方程、Boussinesq方程和耦合的mKdV方程组,说明了具体的求解步骤.比较方便地得到非线性演化方程或方程组的新解析解,如周期解、孤子解等.关键词：Jacobi椭圆函数非线性方程周期解孤子解     

试探方程法及其在非线性发展方程中的应用

提出了一种比较系统的求解非线性发展方程精确解的新方法, 即试探方程法. 以一个带5阶 导数项的非线性发展方程为例, 利用试探方程法化成初等积分形式,再利用三阶多项式的完 全判别系统求解,由此求得的精确解包括有理函数型解, 孤波解, 三角函数型周期解, 多项 式型Jacobi椭圆函数周期解和分式型Jacobi椭圆函数周期解关键词：试探方程法非线性发展方程孤波解Jacobi椭圆函数周期解     

变系数非线性方程的Jacobi椭圆函数展开解

把Jacobi椭圆函数展开法扩展并应用到求解变系数的非线性演化方程,比较方便地得到新的解析解关键词：Jacobi椭圆函数变系数非线性方程类椭圆余弦波解类孤子解     

一般变换下的Jacobi椭圆函数展开法及应用

将在行波变换下的Jacobi椭圆函数展开法推广到范围非常广泛的一般函数变换下进行,利用这一方法求得了一些非线性发展方程的精确周期解,这些解包括了在行波变换下所求得的周期解. 证明了一些非线性发展方程的周期解一定是行波解. 关键词：非线性发展方程周期解行波解Jacobi椭圆函数     

立方非线性Schrdinger方程的Jacobi椭圆函数周期解

本文利用F 展开法 ,求出了立方非线性Schr dinger方程的由Jacobi椭圆函数表示的行波解 ;并且在极限情况下 ,得到了方程的孤波解     

一类非线性方程的新周期解

把Jacobi椭圆函数展开法扩展到Jacobi椭圆余弦函数和第三类Jacobi椭圆函数的有限展开法,并给出了一类非线性波动方程的新周期解,并且应用这种方法得到的周期解也可以退化为冲击波解或孤波解.关键词：Jacobi椭圆函数非线性方程周期解孤波解     

A New Approach to Solve Nonlinear Wave Equations

From the nonlinear sine-Gordon equation, new transformations are obtained in this paper, which are applied to propose a new approach to construct exact periodic solutions to nonlinear wave equations. It is shown that more new periodic solutions can be obtained by this new approach, and more shock wave solutions or solitary wave solutions can be got under their limit conditions.     

Solutions to Generalized mKdV Equation

A transformation is introduced for generalized mKdV (GmKdV for short) equation and Jacobi elliptic function expansion method is applied to solve it. It is shown that GmKdV equation with a real number parameter can be solved directly by using Jacobi elliptic function expansion method when this transformation is introduced, and periodic solution and solitary wave solution are obtained. Then the generalized solution to GmKdV equation deduces to some special solutions to some well-known nonlinear equations, such as KdV equation, mKdV equation, when the real parameter is set specific values.     

Solving Nonlinear Wave Equations by Elliptic Equation

The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.     

Elliptic Equation and Its Direct Applications to Nonlinear Wave Equations

Elliptic equation is taken as an ansatz and applied to solvenonlinear wave equations directly. More kinds of solutions aredirectly obtained, such as rational solutions, solitary wavesolutions, periodic wave solutions and so on. It is shown thatthis method is more powerful in giving more kinds of solutions, soit can be taken as a generalized method.     

Periodic Solutions for Two Coupled Nonlinear-Partial Differential Equations

In this paper, by applying the Jacobi elliptic function expansion method, the periodic solutions for two coupled nonlinear partial differential equations are obtained.     

Applications of Jacobi Elliptic Function Expansion Method for Nonlinear Differential-Difference Equations

The Jacobi elliptic function expansion method is extended to derive the explicit periodic wave solutions for nonlinear differential-difference equations. Three well-known examples are chosen to illustrate the application of the Jacobi elliptic function expansion method. As a result, three types of periodic wave solutions including Jacobi elliptic sine function, Jacobi elliptic cosine function and the third elliptic function solutions are obtained. It is shown that the shock wave solutions and solitary wave solutions can be obtained at their limit condition.