Travelling Wave Solutions of Nonlinear Evolution Equation by Using an Auxiliary Elliptic Equation Method

2012 ◽  
Vol 166-169 ◽  
pp. 3228-3232 ◽  
Author(s):  
Chun Huan Xiang
Keyword(s):  
Elliptic Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Nonlinear Differential Equations ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Equation Method ◽  
Jacobi Elliptic Function ◽  
Travelling Wave Solutions ◽  
Dispersive Waves

The Camassa-Holm and Degasperis-Procesi equation describing unidirectional nonlinear dispersive waves in shallow water is reconsidered by using an auxiliary elliptic equation method. Detailed analysis of evolution solutions of the equation is presented. Some entirely new periodic-soliton solutions, include Jacobi elliptic function solutions, hyperbolic solutions and trigonal solutions, are obtained. The employed auxiliary elliptic equation method is powerful and can be also applied to solve other nonlinear differential equations. This method adds a new route to explore evolution solutions of nonlinear differential equation.

New (3+1)-dimensional nonlinear evolution equation: multiple soliton solutions

2014 ◽  
Vol 4 (4) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Multiple Soliton Solutions ◽  
Simplified Hirota’S Method ◽  
Hirota's Method

AbstractIn this work, we introduce an extended (3+1)-dimensional nonlinear evolution equation. We determine multiple soliton solutions by using the simplified Hirota’s method. In addition, we establish a variety of travelling wave solutions by using hyperbolic and trigonometric ansatze.

scholarly journals The second elliptic equation method for nonlinear equations with variable coefficients

2021 ◽  
pp. 38-38
Author(s):  
Xiaoxia Zhang ◽  
Yanni Zhang ◽  
Jing Pang
Keyword(s):  
Elliptic Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Expansion Method ◽  
Variable Coefficients ◽  
Equation Method ◽  
Jacobi Elliptic Function ◽  
Solitary Wave Solutions ◽  
Rich Solution ◽  
Jacobi Elliptic Function Expansion

The second elliptic equation method is a more general form of Jacobi elliptic function expansion method, which can obtain more kinds of solutions of a nonlinear evolution equation. In this paper, the method is used to solve the Kdv-Burgers-Kuramoto (Benny) equation with variable coefficients, and its extremely rich solution properties are elucidated, among which the biperiodic solutions, solitary wave solutions and trigonometric periodic solutions are analyzed graphically.

Dark and new travelling wave solutions to the nonlinear evolution equation

Optik ◽  
2016 ◽  
Vol 127 (19) ◽  
pp. 8043-8055 ◽  
Author(s):  
Haci Mehmet Baskonus ◽  
Dilara Altan Koç ◽  
Hasan Bulut
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions

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.

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