On a generalized fifth order KdV equations

Abstract In this Letter, we dealt with finding the solutions of a generalized fifth order KdV equation (for short, gfKdV) by using the Adomian decomposition method (for short, ADM). We prove the convergence of ADM applied to the gfKdV equation. Then we obtain the exact solitary-wave solutions and numerical solutions of the gfKdV equation for the initial conditions. The numerical solutions are compared with the known analytical solutions. Their remarkable accuracy are finally demonstrated for the gfKdV equation.

[1]  D. Kaya.  On the solution of a korteweg-de vries like equation by the decomposition method , 1999, Int. J. Comput. Math..

[2]  Y. Cherruault,et al.  Convergence of Adomian's method applied to nonlinear equations , 1994 .

[3]  Salah M. El-Sayed,et al.  An application of the decomposition method for the generalized KdV and RLW equations , 2003 .

[4]  Y. Cherruault,et al.  Practical formulae for the calculus of multivariable adomian polynomials , 1995 .

[5]  Y. Cherruault,et al.  Decomposition methods: A new proof of convergence , 1993 .

[6]  G. Whitham,et al.  Linear and Nonlinear Waves , 1976 .

[7]  Dogan Kaya,et al.  An explicit and numerical solutions of some fifth-order KdV equation by decomposition method , 2003, Appl. Math. Comput..

[8]  M. J. Pujol,et al.  A new formulation of Adomian method: Convergence result , 2001 .

[9]  D. M. Hutton,et al.  Optimisation - Mèthodes locales et globales , 1999 .

[10]  G. Adomian.  A review of the decomposition method in applied mathematics , 1988 .

[11]  Yves Cherruault,et al.  Adomian's polynomials for nonlinear operators , 1996 .

[12]  S. Sawada,et al.  A Method for Finding N-Soliton Solutions of the KdV and KdV-Like Equation , 1974 .

[13]  Wang Yinghai,et al.  The homogeneous balance method, Lax pair, Hirota transformation and a general fifth-order KdV equation , 2002 .

[14]  Y. Cherruault,et al.  New ideas for proving convergence of decomposition methods , 1995 .

[15]  George Adomian,et al.  Solving Frontier Problems of Physics: The Decomposition Method , 1993 .

[16]  D. M. Hutton,et al.  Modèles et méthodes mathématiques pour les sciences du vivant , 1998 .

[17]  B. Duffy,et al.  An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations , 1996 .

[18]  Dogan Kaya,et al.  An application for a generalized KdV equation by the decomposition method , 2002 .

[19]  Sherman X. Bai,et al.  Multiperiod production planning with demand and cost fluctuation , 1998 .

[20]  Y. Cherruault,et al.  New numerical study of Adomian method applied to a diffusion model , 2002 .