Exact Traveling Wave Solutions for the System of Shallow Water Wave Equations and Modified Liouville Equation Using Extended Jacobian Elliptic Function Expansion Method

In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the system of shallow water wave equations and modified Liouville equation which play an important role in mathematical physics.

THE EXTENDED JACOBIAN ELLIPTIC FUNCTION EXPANSION METHOD AND ITS APPLICATIONS IN WEAKLY NONLINEAR WAVE EQUATIONS

The extended Jacobian elliptic function expansion method is introduced and applied to solve the coupled ZK equations and the coupled KP equations describing two weakly long nonlinear wave models in fluid system. Many types of doubly periodic traveling wave solutions are obtained. Under limiting conditions these solutions are reduced into solitary wave solutions.

Extended Jacobian Elliptic Function Expansion Method and Its Applications in Biology

In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to Dynamical system in a new Double-Chain Model of DNA and a diffusive predator-prey system which play an important role in biology.

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.

Some new exact solutions of Jacobian elliptic function about the generalized Boussinesq equation and Boussinesq-Burgers equation

By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions.

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.

(G'/G)-Expansion Method Equivalent to Extended Tanh Function Method

在一篇最近的文章[物理信 A 372 (2008 ) 417 ] ，王等。建议了一个方法，它被叫(G'/G ) 扩大方法，寻找非线性的进化方程的旅行波浪答案。包含 KdV 方程， mKdV 方程，变体 Boussinesq 方程，和 Hirota 一种奶油色的陶器方程的参数的旅行波浪解决方案被使用这个方法获得。他们想(G'/G ) 扩大方法是一个新方法和许多非线性的进化方程的更多的旅行波浪答案能被获得。在这篇论文，我们将证明(G'/G ) 扩大方法等价于扩大 tanh 功能方法。

Jacobian Elliptic Function Method and Solitary Wave Solutions for Hybrid Lattice Equation

在这篇论文，我们成功地扩大了 Jacobian 椭圆形的功能扩大途径到非线性的微分差别的方程。混合格子方程被选择说明这条途径。作为后果，有混合格子方程的不同参数的 Jacobian 椭圆形的函数解决方案的 12 个家庭被获得。什么时候模量 m → 1 或 0，二倍地周期的答案分别地堕落到 solitonic 答案和三角法的功能答案。

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 Schrodinger equation. When the modulous m → 1or 0, doubly-periodic solutions degenerate to solitonic solutions including bright soliton, dark soliton, new solitons as well as trigonometric function solutions.

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.

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。

On a Generalized Extended F-Expansion Method

使用新概括 ansaetz，我们在场为以一个统一方法构造非线性的部分微分方程的准确答案的一个新概括扩大 F-expahsion 方法。在枫树的帮助下使用概括方法，我们考虑(2+1 )-dimentional 碎 soliton 方程。作为结果，我们成功地包括 Jacobi 椭圆形的函数解决方案获得一些新、更一般的解决方案，象 soliton 一样解决方案，三角法的函数解决方案等等。作为一件解说性的样品，碎 soliton 方程的 somesoliton 解决方案的性质被一些数字显示出。我们的方法能也被用于另外的部分微分方程。

New Jacobi Elliptic Function Solutions for the Generalized Nizhnik-Novikov-Veselov Equation

In this paper, a new generalized Jacobi elliptic function expansion method based upon four new Jacobi elliptic functions is described and abundant solutions of new Jacobi elliptic functions for the generalized Nizhnik-Novikov-Veselov equations are obtained. It is shown that the new method is much more powerful in finding new exact solutions to various kinds of nonlinear evolution equations in mathematical physics.

Some New Exact Solutions of Jacobian Elliptic Function of Petviashvili Equation

由使用修改印射的方法，我们发现 Petviashvili 方程的新准确答案。在这篇论文获得的解决方案包括 Jacobian 椭圆形的函数解决方案，联合 Jacobian 椭圆形的函数解决方案， soliton 解决方案，三角形的函数解决方案。

Propagation of traveling wave solutions for nonlinear evolution equation through the implementation of the extended modi ed direct algebraic method

In this work,di erent kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional(3-D)nonlinear evolution equations(NEEs)through the implementation of the modi ed extended direct algebraic method.Bright-singular and dark-singular combo solitons,Jacobi's elliptic functions,Weierstrass elliptic functions,constant wave solutions and so on are attained beside their existing conditions.Physical interpretation of the solutions to the 3-D modi ed KdV-Zakharov-Kuznetsov equation are also given.

Jacobi Elliptic Function Solutions for (2 + 1) Dimensional Boussinesq and Kadomtsev-Petviashvili Equation

(2 + 1) dimensional Boussinesq and Kadomtsev-Petviashvili equation are investigated by employing Jacobi elliptic function expansion method in this paper. As a result, some new forms traveling wave solutions of the equation are reported. Numerical simulation results are shown. These new solutions may be important for the explanation of some practical physical problems. The results of this paper show that Jacobi elliptic function method can be a useful tool in obtaining evolution solutions of nonlinear system.

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.