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Generalized tanh–coth method; generalized (G'/G)-expansion method; Cahn–Hilliard equation; Allen–Cahn equation; steady-state equation.

In this paper, we find exact solutions of some nonlinear evolution equations by using generalized tanh–coth method. Three nonlinear models of physical significance, i.e. the Cahn–Hilliard equation, the Allen–Cahn equation and the steady-state equation with a cubic nonlinearity are considered and their exact solutions are obtained. From the general solutions, other well-known results are also derived. Also in this paper, we shall compare the generalized tanh–coth method and generalized (G'/G )-expansion method to solve partial differentialequations (PDEs) and ordinary differential equations (ODEs). Abundant exact travelling wave solutions including solitons, kink, periodic and rational solutions have been found. These solutions might play important roles in engineering fields. The generalized tanh–coth method was used to construct periodic wave and solitary wave solutions of nonlinear evolution equations. This method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that the generalized tanh–coth method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear problems.

JALIL MANAFIAN¹ MEHRDAD LAKESTANI¹ AHMET BEKIR²

1. Department of Applied Mathematics, Faculty of Mathematical Science, University of Tabriz, Tabriz, Iran
2. Department of Mathematics-Computer, Eski¸sehir Osmangazi University, 26480, Eski¸sehir, Turkey

Published

16 December 2016

Manuscript received

15 July 2015

Manuscript revised

2 February 2016

Accepted

7 March 2016

Early published

4 November 2016