Exact solution of the Biswas-Milovic equation by Adomian decomposition method
About this article
Abstract
This paper studies the exact solution of the Biswas-Milovic equation with Kerr law nonlinearity by the aid of Adomian decomposition method. Biswas-Milovic equation is a generalized version of the familiar nonlinear Schrodinger's equation describing the propagation of solitons through optical fibers for trans-continental and trans-oceanic distances.
References
[1] A. Biswas, D. Milovic, Bright and dark solitons of the generalized nonlinear schrodinger’s equation, commun. nonlinear sci. numer. simul. 15 (5), (2010), 1473-1484.
[2] A. Biswas, S. Konar, Introduction to non-kerr law optical solitons, CRC Press, Boca Raton, FL, USA, 2006.
[3] A. M. Wazwaz, Partial differential equations and solitary waves theory, Springer,(2009).
[4] R. Hirota, Direct method of finding exact solutions of nonlinear evolution equations, in: R. Bullough, P. Caudrey (Eds.), Backlund Transformations, Springer, Berlin, 1980, p. 1157.
[5] V.O. Vakhnenko, E.J. Parkes, A.J. Morrison, A Backlund transformation and the inverse scattering transform method for the generalised Vakhnenko equation, Chaos Soliton Fract. 17 (4), (2003), 683.
View more references (13)
[6] W. Malfliet, W. Hereman, The tanh method. I. Exact solutions of nonlinear evolution and wave equations, Phys. Scripta, 54 ,(1996), 563.
[7] A.M. Wazwaz, The tanh method for travelling wave olutions of nonlinear equations, Appl. Math. Comput. 154 (3), (2004), 713.
[8] A.M. Wazwaz, The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations, Appl. Math. Comput., vol.188 (2), (2007), 1467.
[9] E. Fan, H. Zhang, A note on the homogeneous balance method, Phys. Lett. A ,246, (1998), 403.
[10] A. Bekir, A. Boz, Exact solutions for nonlinear evolution equations using Exp-function method, Phys. Lett. A , 372, (10), (2008), 1619.
[11] G. Adomian, Nonlinear Stochastic Operator Equations, Academic Press, San Diego, (1986).
[12] G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, Boston, (1994).
[13] Y. Cherruault, Convergence of Adomian’s method, Kybernotes, 18(20), (1990), 31-38.
[14] Y. Cherruault and G. Adomian, Decomposition methods: a new proof of convergence,Math. Comput. Modelling, 18 (12), (1993), 103-106 .
[15] A.M. Wazwaz, A reliable modification of Adomian’s decomposition method, Appl. Math. Comput., 92(1), (1998), 1-7.
[16] A.M.Wazwaz, Partial Differential Equations: Methods and Applications, Balkema Publishers, Leiden, (2002).
[17] A.M. Wazwaz, The modified decomposition method for analytic treatment of differential equations, Appl. Math. Comput., 173(1),(2006),165-176.
[18] A.M. Wazwaz, A new algorithm for solving differential equations of the Lane-Emden type, Appl. Math. Comput.,118(2/3), (2001), 287-310.