Extended F-Expansion Method and Periodic Wave Solutions for Klein-Gordon-SchrSdinger Equations

我们在场为在数学物理发现非线性的进化方程的周期的波浪答案的一个扩大 F 扩大方法。由使用扩大 F 扩大方法，各种各样的 Jacobi 椭圆形的功能为 theKlein-Gordon-Schroedinger 方程表示的许多周期的波浪答案被获得。在限制盒子中，方程的独居的波浪解决方案和三角法的函数解决方案也被获得。

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.

Applications of F-expansion to Periodic Wave Solutions for Variant Boussinesq Equations

We present an F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed recently. By using the F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the variant Boussinesq equations. When the modulus m approaches 1 and 0, the hyperbolic function solutions (including the solitary wave solutions) and trigonometric solutions are also given respectively.

Periodic Wave Solutions and Solitary Wave Solutions of the (2+1)-Dimensional Korteweg-de-Vries Equatio

In this paper, we investigate the periodic wave solutions and solitary wave solutions of a (2+1)-dimensional Korteweg-de Vries (KDV) equation by applying Jacobi elliptic function expansion method. Abundant types of Jacobi elliptic function solutions are obtained by choosing different coefficients p, q and r in the elliptic equation. Then these solutions are coupled into an auxiliary equation and substituted into the (2+1)-dimensional KDV equation. As a result, a large number of complex Jacobi elliptic function solutions are obtained, and many of them have not been found in other documents. As , some complex solitary solutions are also obtained correspondingly. These solutions that we obtained in this paper will be helpful to understand the physics of the (2+1)-dimensional KDV equation.

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.

Applications of F-expansion method to the coupled KdV system

An extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics is presented, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed more recently. By using the homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by Jacobi elliptic functions for the coupled KdV equations are derived. In the limit cases, the solitary wave solutions and the other type of travelling wave solutions for the system are also obtained.

Exact Periodic-Wave Solutions to Nizhnik-Novikov-Veselov Equation

Exact periodic-wave solutions to the generalized Nizhnik-Novikov-Veselov (NNV) equation are obtained by using the extended Jacobi elliptic-function method, and in the limit case, the solitary wave solution to NNV equation are also obtained.

Periodic Wave Solutions for Konopelchenko-Dubrovsky Equation

By using F-expansion method proposed recently, we derive the periodic wave solution expressed by Jacobi elliptic functions for Konopelchenko-Dubrovsky equation. In the limit case, the solitary wave solution and other type of the traveling wave solutions are derived.

Solitary Wave Solution of the Two-Dimensional Regularized Long-Wave and Davey-Stewartson Equations in Fluids and Plasmas

This paper investigates the solitary wave solutions of the (2+1)-dimensional regularized long-wave (2DRLG) equation which is arising in the investigation of the Rossby waves in rotating flows and the drift waves in plasmas and (2+1) dimensional Davey-Stewartson (DS) equation which is governing the dynamics of weakly nonlinear modulation of a lattice wave packet in a multidimensional lattice. By using extended mapping method technique, we have shown that the 2DRLG-2DDS equations can be reduced to the elliptic-like equation. Then, the extended mapping method is used to obtain a series of solutions including the single and the combined non degenerative Jacobi elliptic function solutions and their degenerative solutions to the above mentioned class of nonlinear partial differential equations (NLPDEs).

Jacobi Elliptic Function Expansion Method for the Nonlinear Vakhnenko Equation

By using Jacobi elliptic function expansion method, several kinds of travelling wave solutions of Nonlinear Vakhnenko equation are obtained in this paper. As a result, some new forms of traveling wave solutions of the equation are shown, and the numerical simulation with different parameters for the new forms solutions are given.

The Jacobi Elliptic Function Method for Solving Zakharov Equation

The Zakharov equation to describe the laser plasma interaction process has very important sense, this paper gives the solitary wave solutions for Zakharov equation by using Jacobi elliptic function method.

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.

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 。

(2+1)维Nizhnik方程的Jacobi椭圆函数周期解

利用最近提出的 F-展开法,导出了 (2+1) 维 Nizhnik 方程的由 Jacobi 椭圆函数表示的周期解, 并且在极限情况下,可以推得 (2+1) 维 Nizhnik 方程的孤波解以及其他形式解。

非线性方程的Jacobi椭圆函数新周期解

基于刘等(物理学报,2001,50(11):2068-2072.)提出的Jacobi椭圆函数展开方法,将修正的Jacobi椭圆函数展开方法应用于求解修正的BBM方程和结合的KdV-mKdV方程,得到了许多新的用Jacobi椭圆函数表示的周期解,应用该方法得到的周期解在极限情况下可以退化为相应的孤立波解,此方法还可以用于求解其它的非线性方程.

长短波相互作用方程Jacobi椭圆函数新的展开法求解

在原有椭圆函数求解方法的基础上,推广了 Jacobi 椭圆函数展开方法,引入 Jacobi 椭圆函数的负幂次展开研究复非线性演化方程组的求解,得到了更多更新的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.

mBBM方程和KdV方程新的Jacobi椭圆函数周期解

以齐次平衡法J、acobi椭圆函数展开法和辅助方程法为基础,利用第一种椭圆函数方程,把非线性发展方程的形式解取为一种新的形式,用计算机代数系统Mathematica构造了mBBM方程和KdV方程的新的Jacobi椭圆函数周期解.

(2+1)-维破切孤子方程的Jacobi椭圆函数周期解

辅助方程法是求解非线性发展方程的非常有效的方法之一.本文利用辅助方程法,导出(2+1)-维破孤子方程的Jacobi椭圆函数表示的周期解,并且在极限情况下,推得其孤波解及其它形式的解.

双Jacobi椭圆函数展开法及其对KdV方程求解

本文将双Jacobi椭圆函数展开法以及"秩"的概念应用于求解KdV方程,得到了许多组新的用双椭圆函数表示的准确周期解。应用该方法得到的有些周期解在极限情况下可以退化为相应的孤立波解。这种方法还可以用于求解其它非线性波方程。