• Comparison between the generalized tanh–coth and the (G'/G)-expansion methods for solving NPDEs and NODEs

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    • Keywords

       

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

    • Abstract

       

      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.

    • Author Affiliations

       

      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
    • Dates

       
  • Pramana – Journal of Physics | News

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