An improved Jacobian elliptic function expansion method to find new traveling wave solutions for a class of nonlinear wave equations

2016 ◽  
Vol 11 ◽  
pp. 367-375
Author(s):  
Xueqin Zhao
Keyword(s):  
Nonlinear Wave ◽  
Elliptic Function ◽  
Traveling Wave ◽  
Wave Equations ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Nonlinear Wave Equations ◽  
Jacobian Elliptic Function ◽  
Wave Solutions ◽  
Function Expansion

scholarly journals Traveling Wave Solutions of Two Nonlinear Wave Equations by (G′/G)-Expansion Method

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Yazhou Shi ◽  
Xiangpeng Li ◽  
Ben-gong Zhang
Keyword(s):  
Nonlinear Wave ◽  
Traveling Wave ◽  
Wave Equations ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Nonlinear Wave Equations ◽  
Hyperbolic Function ◽  
Exact Traveling Wave Solutions ◽  
Function Solution ◽  
Wave Solutions

We employ the (G′/G)-expansion method to seek exact traveling wave solutions of two nonlinear wave equations—Padé-II equation and Drinfel’d-Sokolov-Wilson (DSW) equation. As a result, hyperbolic function solution, trigonometric function solution, and rational solution with general parameters are obtained. The interesting thing is that the exact solitary wave solutions and new exact traveling wave solutions can be obtained when the special values of the parameters are taken. Comparing with other methods, the method used in this paper is very direct. The (G′/G)-expansion method presents wide applicability for handling nonlinear wave equations.

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

EXACT SOLUTIONS AND THEIR DYNAMICS OF TRAVELING WAVES IN THREE TYPICAL NONLINEAR WAVE EQUATIONS

2009 ◽  
Vol 19 (07) ◽  
pp. 2249-2266 ◽  
Author(s):  
JIBIN LI ◽  
YI ZHANG ◽  
GUANRONG CHEN
Keyword(s):  
Nonlinear Wave ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Wave Equations ◽  
Visual Illusion ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Dynamical Analysis ◽  
Nonlinear Wave Equations ◽  
Wave Solutions

It was reported in the literature that some nonlinear wave equations have the so-called loop- and inverted-loop-soliton solutions, as well as the so-called loop-periodic solutions. Are these true mathematical solutions or just numerical artifacts? To answer the question, this article investigates all traveling wave solutions in the parameter space for three typical nonlinear wave equations from a theoretical viewpoint of dynamical systems. Dynamical analysis shows that all these loop- and inverted-loop-solutions are merely visual illusion of numerical artifacts. To reveal the nature of such special phenomena, this article also offers the mathematical parametric representations of these traveling wave solutions precisely in analytic forms.

BREAKING WAVE SOLUTIONS TO THE SECOND CLASS OF SINGULAR NONLINEAR TRAVELING WAVE EQUATIONS

2009 ◽  
Vol 19 (04) ◽  
pp. 1289-1306 ◽  
Author(s):  
JIBIN LI ◽  
XIAOHUA ZHAO ◽  
GUANRONG CHEN
Keyword(s):  
Dynamical Systems ◽  
Systems Theory ◽  
Nonlinear Wave ◽  
Traveling Wave ◽  
Wave Equations ◽  
Traveling Wave Solutions ◽  
Nonlinear Wave Equations ◽  
Breaking Wave ◽  
Dynamical Behaviors ◽  
Wave Solutions

The existence of breaking wave solutions of the second class of singular nonlinear wave equations is proved by methods from the dynamical systems theory. For the second class of singular nonlinear traveling wave equations, dynamical behaviors of the traveling wave solutions are completely classified and thoroughly discussed. Corresponding to some bounded orbits of the traveling systems, exact parametric representations of traveling wave solutions are derived within different parameter regions of the parameter space.

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