The method for constructing the exact solutions to the nonlinear evolution equation

Taogetusang; Sirendaoerji

doi:10.7498/aps.55.6214

Abstract
Based on tanh-function method, homogeneous balance method and auxiliary equation, a new auxiliary equation was introduced in the paper, meanwhile, a new invariance solution was obtained, and a new exact solitary wave solution for Benjamin-Bona-Mahoney(BBM) equation and modified BBM equation was constructed using the symbolic calculation system of Mathematica. The method introduced in the paper has general significance in searching for exact solutions to the nonlinear developing equation.

Keywords:
new auxiliary equation /

invariance solution /

nonlinear developing equation /

exact solitary wave solution
Authors and contacts
Taogetusang,

Sirendaoerji

1.
内蒙古师范大学数学科学学院, 呼和浩特 010022
References

Cited By

[1]	Taogetusang, Yi Li-Na. New complexion two-soliton solutions of a class of nonlinear evolution equation. Acta Physica Sinica, 2015, 64(2): 020201. doi: 10.7498/aps.64.020201
[2]	Taogetusang. Construction of new infinite sequence complexion soliton-like solutions of nonlinear evolution equations. Acta Physica Sinica, 2013, 62(7): 070202. doi: 10.7498/aps.62.070202
[3]	Taogetusang, Bai Yu Mei. Riemann theta function and other several kinds of new solutions of nonlinear evolution equations. Acta Physica Sinica, 2013, 62(10): 100201. doi: 10.7498/aps.62.100201
[4]	Cheng Jian-Jun, Zhang Hong-Qing. Wronskian solution of general nonlinear evolution equations and Young diagram prove. Acta Physica Sinica, 2013, 62(20): 200504. doi: 10.7498/aps.62.200504
[5]	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
[6]	Taogetusang, Narenmandula. New infinite sequence exact solutions of nonlinear evolution equations with variable coefficients by the second kind of elliptic equation. Acta Physica Sinica, 2011, 60(9): 090201. doi: 10.7498/aps.60.090201
[7]	Taogetusang. A method for constructing infinite sequence complexiton solutions to nonlinear evolution equations. Acta Physica Sinica, 2011, 60(1): 010202. doi: 10.7498/aps.60.010202
[8]	Taogetusang. Several auxiliary equations and infinite sequence exactsolutions to nonlinear evolution equations. Acta Physica Sinica, 2011, 60(5): 050201. doi: 10.7498/aps.60.050201
[9]	Mo Jia-Qi, Zhang Wei-Jiang, He Ming. The solitary wave approximate solution of strongly nonlinear evolution equations. Acta Physica Sinica, 2007, 56(4): 1843-1846. doi: 10.7498/aps.56.1843
[10]	Wu Guo-Jiang, Zhang Miao, Shi Liang-Ma, Zhang Wen-Liang, Han Jia-Hua. The extended expansion method for Jacobi elliptic function and new exact periodic solutions of Zakharov equations. Acta Physica Sinica, 2007, 56(9): 5054-5059. doi: 10.7498/aps.56.5054
[11]	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
[12]	Liu Cheng-Shi. Using trial equation method to solve the exact solutions for two kinds of KdV equations with variable coefficients. Acta Physica Sinica, 2005, 54(10): 4506-4510. doi: 10.7498/aps.54.4506
[13]	Liu Cheng-Shi. Trial equation method and its applications to nonlinear evolution equations. Acta Physica Sinica, 2005, 54(6): 2505-2509. doi: 10.7498/aps.54.2505
[14]	Han Zhao-Xiu. New exact solutions for nonlinear Klein-Gordon equations. Acta Physica Sinica, 2005, 54(4): 1481-1484. doi: 10.7498/aps.54.1481
[15]	Lü Da-Zhao. Abundant Jacobi elliptic function solutions of nonlinear evolution equations. Acta Physica Sinica, 2005, 54(10): 4501-4505. doi: 10.7498/aps.54.4501
[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]	Taogetusang, Sirendaoreji. New exact solitary wave solutions to the BBM and mBBM equations. Acta Physica Sinica, 2004, 53(12): 4052-4060. doi: 10.7498/aps.53.4052
[18]	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
[19]	Xu Gui-Qiong, Li Zhi-Bin. . Acta Physica Sinica, 2002, 51(5): 946-950. doi: 10.7498/aps.51.946
[20]	LIU CHUN-PING. THE SOLITON SOLUTIONS FOR A CLASS OF NONLINEAR COUPLED EQUATIONS. Acta Physica Sinica, 2000, 49(10): 1904-1908. doi: 10.7498/aps.49.1904

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Vol. 55, Issue 12 - 2006-06-20

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