Application of extended simplest equation method to Whitham-Broer-Kaup-Like

Bilige SUDAO; Xiao-min WANG

doi:10.3969/j.issn.1007-5461.2014.02.003

[1] Fan E G, Hon Y C. Applications of extended tanh method to special types of nonlinear equations ［J］. Appl. Math. Comput., 2003, 141: 351-358.

[2] Wang M L, Zhou Y B, Li Z B. Applications of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics ［J］. Phys. Lett. A, 1996, 216: 67-75.

[3] Liu S K, Fu Z T, Liu S D, et al. Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations ［J］. Phys. Lett. A, 2001, 289: 69-74.

[4] Zhang J L, Wang M L, Li X Z. The subsidiary ordinary differential equations and the exact solutions of the higher order dispersive nonlinear Schrdinger equation ［J］. Phys. Lett. A, 2006, 357: 188-195.

[5] Wang M L, Li X Z. Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation ［J］. Chaos, Solitons and Fractals, 2005, 24: 1257-1268.

[6] Wazwaz A M. A sine-cosine method for handling nonlinear wave equations ［J］. Math. Comput. Modelling, 2004, 40 (5-6): 499-508.

[7] Wazwaz A M. Generalized solitonary and periodic solutions for nonlinear partial differential equations by the Exp-function method ［J］. Nonlinear Dyn., 2008, 52: 1-9.

[8] Yan Z Y. Generalized method and its application in the higher-order nonlinear Schrdinger equation in nonlinear optical fibres ［J］. Chaos, Solitons and Fractals, 2003, 16: 759-766.

[9] Kudryashov N A. Simplest equation method to look for exact solutions of nonlinear differential equations ［J］. Chaos, Solitons and Fractals, 2005, 24: 1217-1231.

[10] Kudryashov N A. Exact solitary waves of the Fisher equation ［J］. Phys. Lett. A, 2005, 342: 99-106.

[11] Wang M L, Li X Z, Zhang J L. The (G‘/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics ［J］. Phys. Lett. A, 2008, 372: 417-423.

[12] Yang L J, Yang Q F, Du X Y. New exact solutions of Broer-Kaup-Kupershmidt equation ［J］. Chinese Journal of Quantum Electronics, 2011, 29 (2): 142-146.

[13] Li N, Liu X Q. New explicit solutions of generalized (3+1)-dimensional higher-order Kadomtsov-Petviashivilli equation ［J］. Chinese Journal of Quantum Electronics, 2013, 30 (4): 391-397.

[14] Sun Y Z, Wang Z L, Wang G W, Liu X Q. Soliton solutions for generalized fifth-order KdV and BBM equatins with varible coefficients ［J］. Chinese Journal of Quantum Electronics, 2013, 30 (4): 398-404.

[15] Sudao Bilige, Temuer Chaolu. An extended simplest equation method and its application to several forms of the fifth-order KdV equation ［J］. Appl. Math. Comput., 2010, 216: 3146-3153.

[16] Sudao Bilige, Temuer Chaolu, Wang Xiaomin. Application of the extended simplest equation method to the coupled Schrdinger-Boussinesq equation ［J］. Appl. Math. Comput., 2013, 224: 517-523.

[17] Zhou Y B, Li C. Application of modified (G‘/G)-expansion method to traveling wave solutions for Whitham-Broer-Kaup-Like equations ［J］. Commun. Theor. Phys., 2009, 51(1): 664-670.

[18] Guo S M, Zhou Y B. The extended (G‘/G)-expansion method and its applications to the Whitham-Broer-Kaup-Like equations and coupled Hirota-Satsuma KdV equations ［J］. Appl. Math. Comput., 2010, 215: 3214-3221.

[19] Zhang P. New exact solutions to breaking soliton equations and Whitham-Broer-Kaup equations ［J］. Appl. Math. Comput., 2010, 21(4): 1688-1696.

[20] Broer L J F. Approximate equations for long water waves ［J］. Applied Scientific Research, 1975, 31(5): 377-395.

[21] Abdou M A. The extended tanh method and its applications for solving nonlinear physical models ［J］. Appl. Math. Comput., 2007, 190: 988-996.

[22] Tan F G. New exact traveling wave solutions of Whitham-broer-Kaup-Like equation ［J］. Journal of Inner Mongolia University (Natural Science Edition), 2011, 42(2): 133-140.

[23] Tan F G, Sudao Bilige. More general exact solutions of Whitham-Broer-Kaup-Like equation ［J］. Journal of Inner Mongolia University (Natural Science Edition), 2011, 42(3): 258-264.