scholarly journals Extended Jacobi Elliptic Function Expansion Method to the ZK-MEW Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Weimin Zhang
Keyword(s):  
Solitary Wave ◽  
Elliptic Function ◽  
Expansion Method ◽  
Periodic Wave ◽  
Jacobi Elliptic Function ◽  
Solitary Wave Solutions ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Function Expansion ◽  
Jacobi Elliptic Function Expansion

The extended Jacobi elliptic function expansion method is applied for Zakharov-Kuznetsov-modified equal-width (ZK-MEW) equation. With the aid of symbolic computation, we construct some new Jacobi elliptic doubly periodic wave solutions and the corresponding solitary wave solutions and triangular functional (singly periodic) solutions.

scholarly journals Time Evolution of Folded (2+1)-Dimensional Solitary Waves

2009 ◽  
Vol 64 (5-6) ◽  
pp. 309-314 ◽  
Author(s):  
Song-Hua Ma ◽  
Yi-Pin Lu ◽  
Jian-Ping Fang ◽  
Zhi-Jie Lv
Keyword(s):  
Solitary Wave ◽  
Elliptic Function ◽  
Water Wave ◽  
Periodic Wave ◽  
Wave System ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Variable Separation Approach

Abstract With an extended mapping approach and a linear variable separation approach, a series of solutions (including theWeierstrass elliptic function solutions, solitary wave solutions, periodic wave solutions and rational function solutions) of the (2+1)-dimensional modified dispersive water-wave system (MDWW) is derived. Based on the derived solutions and using some multi-valued functions, we find a few new folded solitary wave excitations.

scholarly journals The First-Integral Method and Abundant Explicit Exact Solutions to the Zakharov Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Yadong Shang ◽  
Xiaoxiao Zheng
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Elliptic Function ◽  
Integral Method ◽  
First Integral ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
First Integral Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions

This paper is concerned with the system of Zakharov equations which involves the interactions between Langmuir and ion-acoustic waves in plasma. Abundant explicit and exact solutions of the system of Zakharov equations are derived uniformly by using the first integral method. These exact solutions are include that of the solitary wave solutions of bell-type fornandE, the solitary wave solutions of kink-type forEand bell-type forn, the singular traveling wave solutions, periodic wave solutions of triangle functions, Jacobi elliptic function doubly periodic solutions, and Weierstrass elliptic function doubly periodic wave solutions. The results obtained confirm that the first integral method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial differential equations.

Investigation of (G'/G)-Expansion Method and Exact Solutions for the (2+1)-Dimensional Calogero-Bogoyavlenskii-Schiff System

2013 ◽  
Vol 432 ◽  
pp. 235-239
Author(s):  
Gen Hai Xu ◽  
Song Hua Ma ◽  
Jian Ping Fang
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
New Family ◽  
Wave Solutions ◽  
Variable Separation Method

With the help of the symbolic computation system Maple and the (G'/G)-expansion method and a linear variable separation method, a new family of exact solutions (including solitary wave solutions,periodic wave solutions and rational function solutions) of the (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff system (2DCBS) is derived.

scholarly journals A New Extended Jacobi Elliptic Function Expansion Method and Its Application to the Generalized Shallow Water Wave Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
Yafeng Xiao ◽  
Haili Xue ◽  
Hongqing Zhang
Keyword(s):  
Shallow Water ◽  
Periodic Solutions ◽  
Elliptic Function ◽  
Water Wave ◽  
Expansion Method ◽  
Jacobi Elliptic Function ◽  
Shallow Water Wave ◽  
Wave Solutions ◽  
Function Expansion ◽  
Jacobi Elliptic Function Expansion

With the aid of symbolic computation, a new extended Jacobi elliptic function expansion method is presented by means of a new ansatz, in which periodic solutions of nonlinear evolution equations, which can be expressed as a finite Laurent series of some 12 Jacobi elliptic functions, are very effective to uniformly construct more new exact periodic solutions in terms of Jacobi elliptic function solutions of nonlinear partial differential equations. As an application of the method, we choose the generalized shallow water wave (GSWW) equation to illustrate the method. As a result, we can successfully obtain more new solutions. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition.

A Variety of Exact Periodic Wave and Solitary Wave Solutions for the Coupled Higgs Equation

2012 ◽  
Vol 67 (10-11) ◽  
pp. 545-549 ◽  
Author(s):  
Houria Trikia ◽  
Abdul-Majid Wazwazb
Keyword(s):  
Solitary Wave ◽  
Soliton Solutions ◽  
Higgs Field ◽  
Periodic Wave ◽  
Travelling Wave ◽  
Jacobi Elliptic Function ◽  
Travelling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Jacobi Elliptic Function Expansion

In this work, the coupled Higgs field equation is studied. The extended Jacobi elliptic function expansion methods are efficiently employed to construct the exact periodic solutions of this model. As a result, many exact travelling wave solutions are obtained which include new shock wave solutions or kink-shaped soliton solutions, solitary wave solutions or bell-shaped soliton solutions, and combined solitary wave solutions are formally obtained.

PERIODIC WAVE SOLUTIONS FOR POCHHAMMER–CHREE EQUATION WITH FIVE ORDER NONLINEAR TERM AND THEIR RELATIONSHIP WITH SOLITARY WAVE SOLUTIONS

2010 ◽  
Vol 24 (19) ◽  
pp. 3769-3783 ◽  
Author(s):  
WEIGUO ZHANG ◽  
YAN ZHAO ◽  
GANG LIU ◽  
TONGKE NING
Keyword(s):  
Solitary Wave ◽  
Nonlinear Term ◽  
Periodic Wave ◽  
Jacobi Elliptic Function ◽  
Solitary Wave Solutions ◽  
Systematic Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Fifth Order ◽  
The Given

In this paper, periodic wave solutions for Pochhammer–Chree equation (PC-equation) with fifth order nonlinear term and their relationship with solitary wave solutions are studied. By designing innovative structure of solution, sixteen bounded periodic wave solutions in fractional form of Jacobi elliptic function (JEF) for PC-equation are given. Furthermore, global phase figure in the plane of the traveling solution for the PC-equation are obtained through dynamic systematic method, we indicate the region in the phase where the given sixteen solutions for PC-equation belong to. We find that two couples of these solutions change into two bell profile solitary wave solutions as k → 1 and four solutions change into four periodic wave solutions in fractional form of cosine function as k → 0. Finally, four figures are shown to describe the evolvement from periodic wave solutions to bell profile solitary wave solutions as k → 1.

scholarly journals Solitary Wave Solutions and Periodic Wave Solutions of theK(m,n)Equation witht-Dependent Coefficients

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Wei Li
Keyword(s):  
Solitary Wave ◽  
Function Method ◽  
Expansion Method ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Periodic Wave Solutions ◽  
Wave Solutions

The Exp-function method combined withF-expansion method is employed to investigate theK(m,n)equation witht-dependent coefficients. The solitary wave solutions and periodic wave solutions to the equation are constructed analytically under certain circumstances. The results presented in this paper improve the previous results.

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