Travelling wave solutions of the Cahn-Allen equation by using first integral method

Abstract In this paper, we established travelling wave solutions of the nonlinear equation. The first integral method was used to construct travelling wave solutions of the Cahn–Allen equation. The obtained results include periodic and solitary wave solutions. The power of this manageable method is confirmed.

[1]  A. Bekir New solitons and periodic wave solutions for some nonlinear physical models by using the sine–cosine method , 2008 .

[2]  M. Ablowitz,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering , 1992 .

[3]  Abdul-Majid Wazwaz,et al.  A sine-cosine method for handlingnonlinear wave equations , 2004, Math. Comput. Model..

[4]  J. Cahn,et al.  A microscopic theory for antiphase boundary motion and its application to antiphase domain coasening , 1979 .

[5]  Abdul-Majid Wazwaz,et al.  The tanh method for traveling wave solutions of nonlinear equations , 2004, Appl. Math. Comput..

[6]  Zhaosheng Feng,et al.  The first-integral method to study the Burgers–Korteweg–de Vries equation , 2002 .

[7]  Ahmet Bekir,et al.  Travelling wave solutions of nonlinear evolution equations by using the first integral method , 2009 .

[8]  K. R. Raslan The first integral method for solving some important nonlinear partial differential equations , 2008 .

[10]  Zhaosheng Feng,et al.  The first integral method to the two-dimensional Burgers–Korteweg–de Vries equation , 2003 .

[11]  A. Bekir The tanh–coth method combined with the Riccati equation for solving non-linear equation , 2009 .

[12]  W. Hereman,et al.  The tanh method: I. Exact solutions of nonlinear evolution and wave equations , 1996 .

[13]  E. Fan,et al.  A note on the homogeneous balance method , 1998 .

[14]  Abdul-Majid Wazwaz,et al.  The extended tanh method for abundant solitary wave solutions of nonlinear wave equations , 2007, Appl. Math. Comput..

[15]  Sheng Zhang,et al.  Application of Exp-function method to a KdV equation with variable coefficients , 2007 .

[16]  E. Fan,et al.  Extended tanh-function method and its applications to nonlinear equations , 2000 .

[17]  Ji-Huan He,et al.  Exp-function method for nonlinear wave equations , 2006 .

[18]  M. A. Abdou,et al.  New exact travelling wave solutions using modified extended tanh-function method , 2007 .

[19]  Ahmet Bekir,et al.  Exact solutions of coupled nonlinear evolution equations , 2008 .

[20]  Abdul-Majid Wazwaz,et al.  The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations , 2007, Appl. Math. Comput..

[21]  A. Bekir,et al.  Exact solutions for nonlinear evolution equations using Exp-function method , 2008 .

[22]  Ryogo Hirota,et al.  Direct method of finding exact solutions of nonlinear evolution equations , 1976 .

[23]  E. J. Parkes,et al.  A Backlund transformation and the inverse scattering transform method for the generalised Vakhnenko equation , 2003 .

[24]  P. Hartman Ordinary Differential Equations , 1965 .