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     

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     

Davey-Stewartson方程组的包络周期解和孤立波解

应用Jacobi椭圆函数展开法,求得了Davey-Stewartson方程组的包络周期解和孤立波解． 关键词： Davey-Stewartson方程 Jacobi椭圆函数 包络周期解 孤立波解     

Jacobi椭圆函数展开法及其在求解非线性波动方程中的应用

给出了Jacobi椭圆函数展开法,且应用该方法获得了几种非线性波方程的准确周期解.该方法包含了双曲函数展开法,应用该方法得到的周期解包含了冲击波解和孤波解. 关键词： Jacobi椭圆函数 非线性方程 周期解 孤波解     

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     

非线性Klein-Gordon方程新的精确解

将行波变换替换为更一般的函数变换,推广了修正的Jacobi椭圆函数展开方法.给出了非线性 Klein-Gordon方程新的周期解.当模m→1或m→0时,这些解退化成相应的孤立波解、三 角函数解和奇异的行波解.对于某些非线性方程,在一定条件下一般变换退化为行波约化. 关键词： Jacobi椭圆函数 非线性发展方程 精确解     

Lam函数和非线性演化方程的扰动方法

利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程.应用Jacobi椭圆函 数展开法求得了零级近似方程的准确解，并由此得到一级近似方程和二级近似方程分别满足 齐次Lam方程和非齐次Lam方程，应用Lam函数和Jacobi椭圆函数展开法可以分别求得一级近似方程和二级近似方程的准确解.这样，就求得了非线性演化方程的多级准确解. 关键词： Jacobi椭圆函数 Lam函数 多级准确解 非线性演化方程 扰动方法     

Lam函数和非线性演化方程的扰动方法

利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程 .应用Jacobi椭圆函数展开法求得了零级近似方程的准确解 ,并由此得到一级近似方程和二级近似方程分别满足齐次Lam 方程和非齐次Lam 方程 ,应用Lam 函数和Jacobi椭圆函数展开法可以分别求得一级近似方程和二级近似方程的准确解 .这样 ,就求得了非线性演化方程的多级准确解 .     

Lamé函数和非线性演化方程的扰动方法

利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程.应用Jacobi椭圆函数展开法求得了零级近似方程的准确解,并由此得到一级近似方程和二级近似方程分别满足齐次Lamé方程和非齐次Lamé方程,应用Lamé函数和Jacobi椭圆函数展开法可以分别求得一级近似方程和二级近似方程的准确解.这样,就求得了非线性演化方程的多级准确解.     

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 Jacobian Elliptic Function Solutions to Modified KdV Equation: I

An extended Jacobian elliptic function expansion method presented recently by us is applied to the mKdV equation such that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu's all results are obtained. When the modulus m→1 or 0, we can find the corresponding six solitary wave solutions and six trigonometric function solutions. This shows that our method is more powerful to construct more exact Jacobian elliptic function solutions and can be applied to other nonlinear differential equations.     

New Jacobian Elliptic Function Solutions of Modified KdV Equation: Ⅱ

Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by usingour extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and anotherthree families of new doubly periodic solutions (Jacobian elliptic function solutions) are fbund again by using a newtransformation, which and our extended Jacobian elliptic function expansion method form a new method still called theextended Jacobian elliptic function expansion method. The new method can be more powertul to be applied to othernonlinear differential equations.     

New Jacobian Elliptic Function Solutions of Modified KdV Equation: II

Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by using our extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and another three families of new doubly periodic solutions (Jacobian elliptic function solutions) are found again by using a new transformation, which and our extended Jacobian elliptic function expansion method form a new method still called the extended Jacobian elliptic function expansion method. The new method can be more powerful to be applied to other nonlinear differential equations.     

New Jacobian Elliptic Function Solutions to Modified KdV Equation: Ⅰ

An extended Jacobian elliptic function expansion method presented recently by us is applied to the mKdVequation such that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu‘s allresults are obtained. When the modulus m → 1 or 0, we can find the corresponding six solitary wave solutions and sixtrigonometric function solutions. This shows that our method is more powerful to construct more exact Jacobian ellipticfunction solutions and can be applied to other nonlinear differential equations.     

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     

非线性发展方程的丰富的Jacobi椭圆函数解

通过把十二个Jacobi椭圆函数分类成四组，提出了新的广泛的Jacobi椭圆函数展开法，利用这一方法求得了非线性发展方程的丰富的Jacobi椭圆函数双周期解.当模数m→0或1时，这些解退化为相应的三角函数解或孤立波解和冲击波解. 关键词： 非线性发展方程 Jacobi椭圆函数 双周期解 行波解     

Symbolic Computation of Extended Jacobian Elliptic Function Algorithm for Nonlinear Differential-Different Equations

The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct more new exact doubly-periodic solutions of the integrable discrete nonlinear Schr ödinger equation. When the modulous m→1 or 0, doubly-periodic solutions degenerate to solitonic solutions including bright soliton, dark soliton, new solitons as well as trigonometric function solutions.     

New Jacobian Elliptic Function Solutions of Modified KdV Equation: Ⅲ

More recently, sixteen families of Jacobian elliptic function solutions of mKdV equation have been foundby using our extended Jacobian elliptic function expansion method. In this paper, we continue to improve our methodby using another eight pairs of the closed Jacobian elliptic functions. The mKdV equation is chosen to illustrate theimproved method such that another eight families of new Jacobian elliptic function solutions are obtained again. Thenew method can be more powerful to be applied to other nonlinear differential equations.