On an Improved Complex Tanh-function Method

On an Improved Complex Tanh-function Method An improved complex tanh-function method is introduced for constructing exact travelling wave solutions for both nonlinear partial differential equations and systems of nonlinear partial differential equations with complex phases and solutions. Keywords: Improved tanh-function method, Complex tanh-function method, Hirota equation, Perturbed Wadati-Segur-Ablowitz equation, coupled Schrodinger-KdV equation. 1 Introduction Recently, a number of methods for finding exact and numerical solutions of nonlinear partial differential equations were presented, such as the truncated Painleve expansion method[l], the Jacobi elliptic function expansion method[2-4], Adomian Pade approximation method[5] and F-expansion method [6-7] etc. The most efficient and straightforward methods to construct exact solutions of partial differential equations are the extended tanhfunction method [8, 9] and the complex tanhfunction method [10]. The purpose of this paper is to improve the complex tanh-function method to find travelling wave solution for equations with complex phases [10, 11], In Section 2, we introduce the improved complex tanh-function method. The improved complex tanh function method is then used to find the solutions of Hirota equation [12] in Section 3. In Section 4, this method is used to find the solution of the perturbed Wadati -Segur-Ablowitz equation [13]. The improved method is also applied to find travelling wave solution http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Nonlinear Sciences and Numerical Simulation de Gruyter

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Publisher
de Gruyter
Copyright
Copyright © 2005 by the
ISSN
1565-1339
eISSN
2191-0294
DOI
10.1515/IJNSNS.2005.6.2.99
Publisher site
See Article on Publisher Site

Abstract

An improved complex tanh-function method is introduced for constructing exact travelling wave solutions for both nonlinear partial differential equations and systems of nonlinear partial differential equations with complex phases and solutions. Keywords: Improved tanh-function method, Complex tanh-function method, Hirota equation, Perturbed Wadati-Segur-Ablowitz equation, coupled Schrodinger-KdV equation. 1 Introduction Recently, a number of methods for finding exact and numerical solutions of nonlinear partial differential equations were presented, such as the truncated Painleve expansion method[l], the Jacobi elliptic function expansion method[2-4], Adomian Pade approximation method[5] and F-expansion method [6-7] etc. The most efficient and straightforward methods to construct exact solutions of partial differential equations are the extended tanhfunction method [8, 9] and the complex tanhfunction method [10]. The purpose of this paper is to improve the complex tanh-function method to find travelling wave solution for equations with complex phases [10, 11], In Section 2, we introduce the improved complex tanh-function method. The improved complex tanh function method is then used to find the solutions of Hirota equation [12] in Section 3. In Section 4, this method is used to find the solution of the perturbed Wadati -Segur-Ablowitz equation [13]. The improved method is also applied to find travelling wave solution

Journal

International Journal of Nonlinear Sciences and Numerical Simulationde Gruyter

Published: Jun 1, 2005

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