Symmetries, reductions and exact solutions of (2+1) dimensional potential Boiti-Leon-Manna-Pempinelli equation

Yong LIU; Xi-qiang LIU; Zhen-li WANG

doi:10.3969/j.issn.1007-5461.2014.05.004

[1] Abdel-All N H, Abdel-Razek M A A, Seddeek A A K. Expanding the tanh-function method for solving nonlinear equations ［J］. Applied Mathematics, 2011, 2(9): 1096-1104.

[2] Parkes E J. Observations on the tanh-coth expansion method for finding solutions to nonlinear evolution equations ［J］. Applied Mathematics and Computation, 2010, 217(4): 1749-1754.

[3] Zhao X Q, Zhi H Y. An improved F-expansion method and its application to coupled Drinfle’d-Sokolov-Wilson equation ［J］. Commun. Theor. Phys., 2008, 50(2): 309-314.

[4] Dimitrova Z I. Discussion on exp-function method and modified method of simplest equation ［J］. arXiv preprint arXiv, 2013, 13(03): 0122.

[5] Bhrawy A H, Abdelkawy M A, Biswas A. Cnoidal and snoidal wave solutions to coupled nonlinear wave equations by the extended Jacobi’s elliptic function method ［J］. Communications in Nonlinear Science and Numerical Simulation, 2013, 18(4): 915-925.

[6] Wang Mingliang. Exact solutions for a compound KdV-Burgers equation ［J］. Physics Letters A, 1996, 213(5): 279-287.

[9] Molati Motlatsi, Chaudry Masood Khalique. Symmetry classification and invariant solutions of the variable coefficient BBM equation ［J］. Applied Mathematics and Computation, 2013, 219(15): 7917-7922.

[10] Dai Chaoqing, Zhou Guoquan. Exotic interactions between solitons of the (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov system ［J］. Chinese Physics, 2007, 1(5): 1201.

[11] Wang Ling, Dong Zhongzhou, Liu Xiqiang. Symmetry reductions, exact solutions and conservation laws of asymmetric Nizhnik-Novikov-Veselov equation ［J］. Communications in Theoretical Physics, 2008, 49(1): 1.

[12] Estevez P G, Leble S. A wave equation in 2+1: Painleve analysis and solutions ［J］. Inverse Problems, 1995, 11(4): 925.

[13] Tang Xiaoyan, Lou Senyue, Zhang Ying. Localized excitations in (2+1)-dimensional systems ［J］. Physical Review E, 2002, 6(4): 046601.

[16] Shi L M, Zhang L F, Meng H, et al. A method to construct Weierstrass elliptic function solution for nonlinear equations ［J］. International Journal of Modern Physics B, 2011, 25(14): 1931-1939.

[17] Adem A R, Khalique C M. Symmetry reductions, exact solutions and conservation laws of a new coupled KdV system ［J］. Communications in Nonlinear Science and Numerical Simulation, 2012, 17(9): 3465-3475.

[18] Moleleki L D, Johnpillai A G, Khalique C M. Symmetry reductions and exact solutions of a variable coefficient (2+1)-Zakharov-Kuznetsov equation ［J］. Mathematical and Computational Applications, 2012, 17(2): 132.