Exact solution of the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation by Adomian decomposition method

Iftikhar Ahmed; Chunlai Mu; Pan Zheng

doi:10.26637/mjm202/008

Abstract

This paper studies the exact solution of the the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation by the aid of Adomian decomposition method.

Keywords:

Exact solution, Hyperbolic Schrödinger equation, Adomian decomposition method

Mathematics Subject Classification:

83C15, 35L70, 49M27

Authors Imprint References Funding Related Articles Downloads

Iftikhar Ahmed College of Mathematics and Statistics, Chongqing University, Chongqing 401331, PR China.
Chunlai Mu College of Mathematics and Statistics, Chongqing University, Chongqing 401331, PR China.
Pan Zheng College of Mathematics and Statistics, Chongqing University, Chongqing 401331, PR China.

Pages: 160-164
Date Published: 01-04-2014
Vol. 2 No. 02 (2014): Malaya Journal of Matematik (MJM)

S.P. Gorz, P.K. Ockaert, P. Emplit, and M. Haelterman, Oscillatory neck instability of spatial bright solitons in hyperbolic systems, Physical Review Letters, 102(13)(2009), 134101-134104. DOI: https://doi.org/10.1103/PhysRevLett.102.134101

A. Biswas, S. Konar, Introduction to Non-Kerr Law Optical Solitons, CRC Press, Boca Raton, FL, USA, 2006. DOI: https://doi.org/10.1201/9781420011401

A. M. Wazwaz, Partial Differential Equations and Solitary Waves Theory, Springer, 2009. DOI: https://doi.org/10.1007/978-3-642-00251-9

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.

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), 683–692. DOI: https://doi.org/10.1016/S0960-0779(02)00483-6

W. Malfliet, W. Hereman, The tanh method. I. Exact solutions of nonlinear evolution and wave equations, Phys. Scripta 54 (1996), 563-568. DOI: https://doi.org/10.1088/0031-8949/54/6/003

A.M. Wazwaz, The tanh method for travelling wave olutions of nonlinear equations, Appl. Math. Comput., 154 (3), (2004), 713-723. DOI: https://doi.org/10.1016/S0096-3003(03)00745-8

A.M. Wazwaz, The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations, Appl. Math. Comput., 188(2)(2007), 1467-1475. DOI: https://doi.org/10.1016/j.amc.2006.11.013

E. Fan, H. Zhang, A note on the homogeneous balance method, Phys. Lett., A(246)(1998), 403-406. DOI: https://doi.org/10.1016/S0375-9601(98)00547-7

A. Bekir, A. Boz, Exact solutions for nonlinear evolution equations using Exp-function method, Phys. Lett., A(372)(10)(2008), 1619-1625. DOI: https://doi.org/10.1016/j.physleta.2007.10.018

G. Adomian, Nonlinear Stochastic Operator Equations, Academic Press, San Diego, 1986. DOI: https://doi.org/10.1016/B978-0-12-044375-8.50012-5

G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, Boston, 1994. DOI: https://doi.org/10.1007/978-94-015-8289-6

Y. Cherruault, Convergence of Adomian’s method, Kybernotes, 18(20)(1990), 31-38. DOI: https://doi.org/10.1108/eb005812

Y. Cherruault and G. Adomian, Decomposition methods: a new proof of convergence, Math. Comput. Modelling, 18(12)(1993), 103-106 . DOI: https://doi.org/10.1016/0895-7177(93)90233-O

A.M. Wazwaz, A reliable modification of Adomian’s decomposition method, Appl. Math. Comput., 92(1)(1998), 1-7.

A.M.Wazwaz, Partial Differential Equations: Methods and Applications, Balkema Publishers, Leiden, 2002.

A.M.Wazwaz, The modified decomposition method for analytic treatment of differential equations, Appl. Math. Comput., 173(1)(2006), 165-176. DOI: https://doi.org/10.1016/j.amc.2005.02.048

A.M. Wazwaz, A new algorithm for solving differential equations of the Lane-Emden type, Appl. Math. Comput., 118(2/3)(2001), 287-310. DOI: https://doi.org/10.1016/S0096-3003(99)00223-4