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Abstract
In this paper, several new exact solitary wave solutions to the BBM and the m BBM equations are constructed explicitly by combined use of a hyperbolic functio n assumption and a new auxiliary ordinary differential equation. This method also can be used to find new solitary wave solutions to other nonlinear evolution equ ations.

Keywords:
auxiliary equation/

hyperbolic function assumption/

solitary wave sol utions
Authors and contacts
Taogetusang,

Sirendaoreji

1.
References

Cited By

[1]	Xu Yuan-Fen.Exact traveling wave solutions for simplified model of Gross-Pitaevskii equation in the 1D-Tonks-Girardeau gas. Acta Physica Sinica, 2013, 62(10): 100202.doi:10.7498/aps.62.100202
[2]	Taogetusang, Bai Yu-Mei.A method of constructing infinite sequence soliton-like solutions of nonlinear evolution equations. Acta Physica Sinica, 2012, 61(13): 130202.doi:10.7498/aps.61.130202
[3]	Taogetusang.Infinite sequence peak solitary wave solutions ofDegasperis-Procesi equation. Acta Physica Sinica, 2011, 60(7): 070204.doi:10.7498/aps.60.070204
[4]	Taogetusang.New infinite sequences exact solutions to sine-Gordon-type equations. Acta Physica Sinica, 2011, 60(7): 070203.doi:10.7498/aps.60.070203
[5]	Yang Pei, Chen Yong, Li Zhi-Bin.Analytic approximation for the soliton solution of the discrete modified KdV equation. Acta Physica Sinica, 2010, 59(6): 3668-3673.doi:10.7498/aps.59.3668
[6]	Li Bang-Qing, Ma Yu-Lan.(G′/G)-expansion method and new exact solutions for (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov system. Acta Physica Sinica, 2009, 58(7): 4373-4378.doi:10.7498/aps.58.4373
[7]	Taogetusang, Sirendaoerji.Constructing new exact solutions to nonlinear difference-differential equations by Riccati equation. Acta Physica Sinica, 2009, 58(9): 5894-5902.doi:10.7498/aps.58.5894
[8]	Taogetusang, Sirendaoerji.A method for constructing exact solutions of nonlinear evolution equation with variable coefficients. Acta Physica Sinica, 2009, 58(4): 2121-2126.doi:10.7498/aps.58.2121
[9]	Gao Bin, Liu Shi-Da, Liu Shi-Kuo.Envelope periodic and solitary solutions of Davey-Stewartson equation. Acta Physica Sinica, 2009, 58(4): 2155-2158.doi:10.7498/aps.58.2155
[10]	Taogetusang, Sirendaoerji.The new exact solutions of Volterra difference-differential equation and KdV difference-differential equation. Acta Physica Sinica, 2009, 58(9): 5887-5893.doi:10.7498/aps.58.5887
[11]	Taogetusang, Sirendaoerji.The auxiliary equation for constructing the exact solutions of the variable coefficient combined KdV equation with forcible term. Acta Physica Sinica, 2008, 57(3): 1295-1300.doi:10.7498/aps.57.1295
[12]	.Solving solitary wave solutions of higher dimensional nonlinear evolution equations with the homotopy analysis method. Acta Physica Sinica, 2007, 56(12): 6791-6796.doi:10.7498/aps.56.6791
[13]	Yang Hong-Juan, Shi Yu-Ren, Duan Wen-Shan, Lü Ke-Pu.Solving solitary wave solutions of nonlinear evolution equations with the homotopy analysis method. Acta Physica Sinica, 2007, 56(6): 3064-3069.doi:10.7498/aps.56.3064
[14]	Taogetusang, Sirendaoerji.Constructing the exact solutions of the (2+1)-dimensional Hybrid-Lattice and discrete mKdV equation. Acta Physica Sinica, 2007, 56(2): 627-636.doi:10.7498/aps.56.627
[15]	Taogetusang, Sirendaoerji.New exact solitary wave solutions for nonlinear wave equation with fifth-order strong nonlinear term constructed by hyperbolic function type of auxiliary equation. Acta Physica Sinica, 2006, 55(1): 13-18.doi:10.7498/aps.55.13
[16]	Huang Ding-Jiang, Zhang Hong-Qing.Extended hyperbolic function method and new exact solitary wave solutions of Zakharov equations. Acta Physica Sinica, 2004, 53(8): 2434-2438.doi:10.7498/aps.53.2434
[17]	Zhang Shan-Qing, Li Zhi-Bin.A new application of Jacobi elliptic function expansion method. Acta Physica Sinica, 2003, 52(5): 1066-1070.doi:10.7498/aps.52.1066
[18]	Shi Yu-ren, Lü Ke-Pu, Duan Wen-Shan, Hong Xue-Ren, Zhao Jin-Bao, Yang Hong-Juan.Explicit and exact solutions of the combined KdV equation. Acta Physica Sinica, 2003, 52(2): 267-270.doi:10.7498/aps.52.267
[19]	Guo Guan-Peng, Zhang Jie-Fang.. Acta Physica Sinica, 2002, 51(6): 1159-1162.doi:10.7498/aps.51.1159
[20]	TAO FU-ZHEN, LI BO.A SET OF EXACT GRAVITATIONAL 2-SOLITON SOLUTIONS OF EINSTEIN'S EQUATIONS. Acta Physica Sinica, 1989, 38(5): 753-760.doi:10.7498/aps.38.753

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Vol. 53, Issue 12 - 2004-06-20

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