A numerical method for solving Jaulent-Miodek equation

Abstract This Letter presents a numerical method, based on the Adomian's decomposition method (ADM), is presented of the Jaulent–Miodek (JM) equation. We obtain the numerical and exact travelling wave solutions of the JM equation for the initial conditions. The ADM method provides a better approximation to the exact solution than the classical methods. In order to show the efficiency of this method, exhaustive numerical examples are presented.

[1]  Yuzhu Wang,et al.  Bogoliubov Quasiparticles Carried by Dark Solitonic Excitations in Nonuniform Bose-Einstein Condensates , 1998 .

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

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

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

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

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

[7]  C. Uberoi,et al.  Explosion of soliton in a multicomponent plasma , 1997 .

[8]  Abdul-Majid Wazwaz,et al.  Partial differential equations : methods and applications , 2002 .

[9]  Salah M. El-Sayed,et al.  On a generalized fifth order KdV equations , 2003 .

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

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

[12]  S. Lou,et al.  A Direct Perturbation Method: Nonlinear Schrödinger Equation with Loss , 1999 .

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

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

[15]  Jie-fang Zhang.  Multiple Soliton Solutions of the Dispersive Long-Wave Equations , 1999 .

[16]  E. Fan,et al.  Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics , 2003 .

[17]  Y. Cherruault.  Convergence of Adomian's method , 1989 .