The extended tanh method for abundant solitary wave solutions of nonlinear wave equations

2007 ◽  
Vol 187 (2) ◽  
pp. 1131-1142 ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Solitary Wave ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Nonlinear Wave Equations ◽  
Solitary Wave Solutions ◽  
Extended Tanh Method ◽  
Wave Solutions ◽  
Tanh Method

scholarly journals Study on New Doubly-periodic Solutions of two Coupled Nonlinear Wave Equations in Complex and Real Fields

2004 ◽  
Vol 59 (1-2) ◽  
pp. 29-34 ◽  
Author(s):  
Zhenya Yan
Keyword(s):  
Solitary Wave ◽  
Periodic Solutions ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Scalar Fields ◽  
Nonlinear Wave Equations ◽  
Solitary Wave Solutions ◽  
Real Scalar ◽  
Wave Solutions

In this paper, new doubly-periodic solutions in terms of Weierstrass elliptic functions are investigated for the coupled nonlinear Schr¨odinger equation and systems of two coupled real scalar fields. Solitary wave solutions are also given as simple limits of doubly periodic solutions. - PACS: 03.40.Kf; 02.30Ik

scholarly journals Water Wave Solutions of the Coupled System Zakharov-Kuznetsov and Generalized Coupled KdV Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
A. R. Seadawy ◽  
K. El-Rashidy
Keyword(s):  
Solitary Wave ◽  
Traveling Wave Solutions ◽  
Coupled System ◽  
Solitary Wave Solutions ◽  
Coupled Partial Differential Equations ◽  
Extended Tanh Method ◽  
Kdv Equations ◽  
Wave Solutions ◽  
Tanh Method ◽  
Coupled Kdv Equations

An analytic study was conducted on coupled partial differential equations. We formally derived new solitary wave solutions of generalized coupled system of Zakharov-Kuznetsov (ZK) and KdV equations by using modified extended tanh method. The traveling wave solutions for each generalized coupled system of ZK and KdV equations are shown in form of periodic, dark, and bright solitary wave solutions. The structures of the obtained solutions are distinct and stable.

scholarly journals Exact Solitary Wave and Periodic Wave Solutions of a Class of Higher-Order Nonlinear Wave Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Lijun Zhang ◽  
Chaudry Masood Khalique
Keyword(s):  
Solitary Wave ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Kdv Equation ◽  
Periodic Wave ◽  
Sixth Order ◽  
Nonlinear Wave Equations ◽  
Lax Equation ◽  
Periodic Wave Solutions ◽  
Wave Solutions

We study the exact traveling wave solutions of a general fifth-order nonlinear wave equation and a generalized sixth-order KdV equation. We find the solvable lower-order subequations of a general related fourth-order ordinary differential equation involving only even order derivatives and polynomial functions of the dependent variable. It is shown that the exact solitary wave and periodic wave solutions of some high-order nonlinear wave equations can be obtained easily by using this algorithm. As examples, we derive some solitary wave and periodic wave solutions of the Lax equation, the Ito equation, and a general sixth-order KdV equation.

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