NONLINEAR EVOLUTION EQUATIONS IN VIEW OF THE EXP-FUNCTION METHOD AND ITS GENERALIZATION

• Published in: International journal of evolution equations Vol. 7; no. 1; p. 1
• Main Authors: Ebaid, Abdelhalim, Aly, Emad
• Format: Journal Article
• Language: English
• Published: Hauppauge Nova Science Publishers, Inc 01.01.2012
• Subjects: Differential equations; Evolution; Exact solutions; Functions (mathematics); Klein-Gordon equation; Mathematical analysis; Nonlinear evolution equations; Nonlinearity
• ISSN: 1549-2907

Nonlinear phenomena are usually governed by nonlinear ordinary or partial differential equations with prescribed boundary conditions. The nonlinear evolution equations of mathematical physics are major subjects in physical science. The main goal of mathematicians and physicists is to seek for the exact solutions for such nonlinear differential equations. In order to achieve this aim, many methods have been proposed during the past two decades; such as tanh-function, Jacobi-elliptic function, F-expansion, Exp-function and its generalization, named as ...-function method. In this article, the authors show the advantages of the Exp-function and the ...-function methods over the other methods. They analyze also their applications to several nonlinear evolution equations, nonlinear KdV equation, Burgers' equation, the combined KdV-mKdV equation, the generalized Klein-Gordon equation, and some other nonlinear evolution equations with variable coefficients and nonlinear terms of any orders. Application of the ...-function method to solve a third order nonlinear differential equations describing the nano boundary layer flow is also discussed. (ProQuest: ... denotes formulae/symbols omitted.)