Application of the exp-function method for solving nonlinear reaction–diffusion equations arising in mathematical biology

Abstract

a b s t r a c tIn this work we consider nonlinear reaction-diffusion equations arising in mathematical biology. We use the exp-function method in order to obtain conventional solitons and periodic solutions. The proposed scheme can be applied to a wide class of nonlinear equations.

A Note on Exact Travelling Wave Solutions for the Klein–Gordon– Zakharov Equations

“…More details are presented in [15]. c 2012 Verlag der Zeitschrift für Naturforschung, Tübingen · http://znaturforsch.com Quite recently, based on the trigonometric-function series method [2] and the exp-function method [16], Zhang et al [17] proposed a new method called the modified trigonometric function series method (MTFSM) to construct travelling wave solutions of the perturbed nonlinear Schrödinger equation (NLSE) with Kerr law nonlinearity:…”

A Numerical Study of the Nonlinear Reaction-Diffusion Equation with Different Type of Absorbent Term by Homotopy Analysis Method

“…In 2010, Yıldırım and Pınar [10] discussed the application of the exp-function method for solving the nonlinear reaction diffusion equation which is arising in the mathematical biology. Mishra and Kumar [11] introduced the exact solutions for a variable coefficient nonlinear diffusion-reaction equation with a nonlinear convective term.…”

A Note on Exact Solutions of Coupled (2+1)-dimensional Nonlinear Systems of Schr{\" o}dinger Equations

“…The wave phenomena are observed in fluid dynamics, plasma, elastic media, optical fibres, etc. In the recent years, many direct methods have been developed to obtain traveling wave solutions to the nonlinear partial differential equations (NLPDEs), such as the trigonometric function series method (Zhang, 2008;Ma & Fuchssteiner, 1996), the modified mapping method and the extended mapping method (Zhang, Liu, Miao, & Chen, 2010), the modified trigonometric function series method (Zhang, Li, Liu, & Miao, 2011), the dynamical system approach and the bifurcation method (Zhang, Liu, Miao, & Chen, 2011;Zhang, Gan, & Yu, 2011), the exp-function method (Yıldırım, & Pınar, 2010;Khani, Darvishi, Farmany, & Kavitha, 2010), the multiple exp-function method (Ma, Huang, & Zhang, 2010), the transformed rational function method (Ma & Lee, 2009), the symmetry algebra method (consisting of Lie point symmetries) (Ma & Chen, 2009), the Wronskian technique (Ma & You, 2005),the modified ( G G )-expansion method and so on. In this paper, we constuct new exact traveling solutions to the coupled (2+1)-dimensional nonlinear systems of Schrödinger equations given in Khani, Darvishi, Farmany and Kavitha (2010).…”

“…Quite recently, by the trigonometric-function series method (Zhang, 2008) and the exp-function method (Yıldırım & Pınar, 2010;Khani, Darvishi, Farmany, & Kavitha, 2010), proposed a new method called the modified trigonometric function series method(MTFSM) to obtain traveling wave solutions to the perturbed nonlinear Schrödinger's equation (NLSE) with Kerr law nonlinearity as follows…”