A method for constructing exact solutions of nonlinear evolution equation with variable coefficients

Taogetusang; Sirendaoerji

doi:10.7498/aps.58.2121

Abstract
A function transformation method for constructing exact solutions of the variable coefficient nonlinear evolution equations is proposed. The method together with the the second kind of elliptic equation and the symbolic computation system Mathematica is used to construct the new exact Jacobi elliptic function solutions, the degenerated soliton-like solutions and trigonometric function solutions of the composed KdV equation with forced variable coefficients.

Keywords:
auxiliary equation /

function transformation /

nonlinear evolution equation with variable coefficients /

exact 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]	Liu Yong, Liu Xi-Qiang. Exact solutions of Whitham-Broer-Kaup equations with variable coefficients. Acta Physica Sinica, 2014, 63(20): 200203. doi: 10.7498/aps.63.200203
[2]	Wan Hui. Exact solutions to the nonlinear diffusion-convection equation with variable coefficients and source term. Acta Physica Sinica, 2013, 62(9): 090203. doi: 10.7498/aps.62.090203
[3]	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
[4]	Taogetusang, Bai Yu-Mei. New type infinite sequence exact solutions of the second KdV equation with variable coefficients. Acta Physica Sinica, 2012, 61(6): 060201. doi: 10.7498/aps.61.060201
[5]	Taogetusang. New infinite sequences exact solutions to sine-Gordon-type equations. Acta Physica Sinica, 2011, 60(7): 070203. doi: 10.7498/aps.60.070203
[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. New infinite sequence exact solutions to the general lattice. Acta Physica Sinica, 2010, 59(10): 6712-6718. doi: 10.7498/aps.59.6712
[8]	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
[9]	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
[10]	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
[11]	Mao Jie-Jian, Yang Jian-Rong. New solitary-wave-like solutions and exact solutions to variable coefficient generalized KdV equation. Acta Physica Sinica, 2007, 56(9): 5049-5053. doi: 10.7498/aps.56.5049
[12]	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
[13]	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
[14]	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
[15]	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
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[18]	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
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[20]	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

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Vol. 58, Issue 4 - 2009-02-20

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A method for constructing exact solutions of nonlinear evolution equation with variable coefficients

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A method for constructing exact solutions of nonlinear evolution equation with variable coefficients

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