Symmetry reduction and exact solutions of generalized fourth-order dispersive equation

Zhen-li WANG; Xi-qiang LIU

doi:10.3969/j.issn.1007461.2014.03.002

[1] He J H, Wu X H. Exp-function method for nonlinear wave equation ［J］. Chaos Solitons and Fractals, 2006, 3(11): 700-708.

[2] Wang M L. Exact solutions of a compound KdV-Burgers equation ［J］. Phys. Lett. A, 1996, 213(5): 279-287.

[3] Liu J, Yang K. The extended F-expansion method and exact solutions of nonlinear PDEs ［J］.Chaos Solitons Fractals, 2004, 22(1): 111-121.

[4] Wazwaz A M. The tanh method for travelling wave solution of nonlinear wave equations ［J］. Appl. Math. Comput., 2007, 187(2): 1131-1142.

[5] Fan E G, Zhang J. Applications of the Jacobi elliptic function method to special-type nonlinear equations ［J］. Phys. Lett. A, 2002, 305(6): 383-392.

[6] Fu Z T, Liu S K, Liu S D, et al. New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations ［J］. Phys. Lett. A, 2001, 290(1): 72-76.

[7] Xin X P, Liu X Q, Zhang L L. Explicit solutions of the BK equation ［J］. Applied Mathematics and Computation, 2010, 215(10): 3669-3673.

[8] Liu N, Liu X Q. Similarity reductions and similarity solutions of the (3+1)-dimensional Kadomtsev-Petviashvili equation ［J］. Chinese Physics Letters, 2008, 25(10): 3527-3530.

[9] Wang L, Liu X Q, Dong Z Z. Study of (2+1)-dimensional higher-order Broer-Kaup system ［J］. Communications in Theoretical Physics, 2007, 47(3): 403-408.

[12] Miao Q, Xin X P, Chen Y. Nonlocal symmetries and explicit solutions of the AKNS system ［J］. Applied Mathematics Letters, 2014, 28 : 7-13.

[13] Wazwaz A M. Compactons in a class of nonlinear dispersive equations ［J］. Mathematical and Computer Modelling, 2003, 37(3) : 333-341.

[14] Johnpillai A G, Khalique C M, Biswas A. Exact solutions of KdV equation with time-dependent coefficients ［J］. Applied Mathematics and Computation, 2010, 21(10): 3114-3119.

[15] Nail H. Ibragimov. A new conservation theorem ［J］. Math. Anal. Appl., 2007, 333(1): 311-328.

[16] Xin X P, Liu X Q, Zhang L L, Symmetry reduction, exact solutions and conservation laws of the Sawada-Kotera-Kadomtsev-Petviashvili equation ［J］. Applied Mathematics and Computation, 2010, 21(4):1065-1071.

[17] Wang G W , Liu X Q, Zhang Y Y, Symmetry reduction, exact solutions and conservation laws of a new fifth-order nonlinear integrable equation ［J］.Communications in Nonlinear Science and Numerical Simulation, 2013, 18: 2313-2320.