Description of a wave-wave interaction model by Variational and Decomposition methods

[1] L. Debtnath, Nonlinear Partial Differential Equations for Scientist and Engineers, Birkhauser, Boston, MA, 1997.
[2] A.M. Wazwaz, Partial Differential Equations: Methods and Applications, Balkema, Rotterdam,
2002.
[3] J.H. He, Some asymptotic methods for strongly nonlinear equations, Int. J. Modern Phys. B 20 (10) (2006)1141-1199.
[4] S. Momani, Z. Odibat, Analytical approach to linear fractional partial differential equations arising in fluid mechanics, Phys. Lett. A 1 (53)(2006) 1-9.
Description of a wave-wave interaction model
63
[5] A.M.Wazwaz, A new method for solving singular initial value problems in the second order differential equations, Appl. Math. Comput. 128 (2002) 47-57.
[6] M.A. Abdou, A.A. Soliman, Variational iteration method for solving Burger's and coupled Burger's equations, J. Comput. Appl. Math. 181 (2) (2005) 245-251.
[7] E. Fan, Y.C. Hon, Applications of extended tanh method to special types of nonlinear equations, Appl. Math. Comput., in press.
[8] J.H. He, A variational iteration approach to nonlinear problems and its applications, Mech. Appl. 20 (1) (1998) 30-31.
[9] J.H. He, Variational iteration method—a kind of nonlinear analytical technique: some examples, International J. Nonlinear Mech 34 (1999)708-799.
[10] J.H. He, Variational iteration method for autonomous ordinary differential systems, Appl. Math. Comput. 114 (2/3) (2000) 115-123.
[11] A.M.Wazwaz, A new technique for calculating Adomian polynomials for nonlinear polynomials, Appl. Math. Comput. 111 (1) (2000) 33-51.
[16] G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, Boston,
1994.
[13] G. Adomian, A review of the decomposition method in applied mathematics, J. Math. Anal. Appl. 135 (1988) 501-544.
[14] D. Kaya, S.M. El-Sayed, On a generalized fifth order KdVequation, Phys. Lett. A 310(2003) 44-51
[15] D. Kaya, S.M. El-Sayed, An application of the generised decomposition method for the generlised KdV and RLW equations, Chaos Solitons Fractals 17 (2003) 869-77
[16] J.H. He, A new approach to nonlinear partial differential equations, Comm. Nonlinear Sci Numer. Simul. 2 (4) (1997) 203-205.
[17] A.M. Wazwaz, Necessary conditions for the appearance of noise terms in decomposition solution series, Appl. Math. Comput. 81 (1997)265-274.
[18] A.M.Wazwaz, The decomposition method for solving the diffusion equation subject to the classification of mass, Internat. J. Appl. Math. 3 (1)(2000) 25-34.
[19] Arun Kumar, An analytical solution for a coupled partial differential equation, Applied Mathematics and Computation, vol.212, No.1, (2009) 245-250
[20] Y. Cherruault, Convergence of Adomian's method, Mathematical and Computer Modelling Volume 14(C), (1990)83-86
[21] K. Abbaoui, M.J. Pujol, Y. Cherruault, N. Himoun, P. Grimalt, A new formulation of Adomian method: Convergence result, Kybernetes 30 (2001) 1183-1191
[22] K. Abbaoui, Y. Cherruault, New ideas for proving convergence of decomposition methods, Comput. Math. Appl. 29 (1995) 103-108.
[23] Zhang, X., A modification of the Adomian decomposition method for a class of nonlinear singular boundary value problems, J.Comp. & App Math. 180(2) 2, (2005),377-389