The N-soliton-like solution and B&auml;cklund transformation for a non-isospectral and variable-coefficient modified Korteweg-de Vries equation

Qian Feng; Xiang-Hua Meng; Xin Yu; Zhi-Yuan Sun; Tao Xu; Bo Tian; Yi-Tian Gao

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The N-soliton-like solution and Bäcklund transformation for a non-isospectral and variable-coefficient modified Korteweg-de Vries equation

Qian Feng 1 #,Xiang-Hua Meng 2,Xin Yu 1,Zhi-Yuan Sun 1,Tao Xu 2,Bo Tian 2,Yi-Tian Gao 1 *

1.Beijing University of Aeronautics and Astronautics

2.Beijing University of Posts and Telecommunications

*Correspondence author

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Funding: the Key Project of Chinese Ministry of Education,教育部博士点基金，国家自然科学基金，973项目（No.106033,20060006024,60772023 and 60372095，2005CB321901）

Opened online: 6 May 2008

Accepted by: none

Citation: Qian Feng,Xiang-Hua Meng,Xin Yu.The N-soliton-like solution and Bäcklund transformation for a non-isospectral and variable-coefficient modified Korteweg-de Vries equation[OL]. [ 6 May 2008] http://en.paper.edu.cn/en_releasepaper/content/21172

As an important model mathematically and physically, a non-isospectral and variable-coefficient modified Korteweg-de Vries (mKdV) equation is investigated in this paper. Starting from the Lax pair presented, the Bäcklund transformation in original variables is explicitly deduced. And then, by a dependent variable transformation, the non-isospectral and variable-coefficient mKdV equation is transformed into bilinear equations, by virtue of which the N-soliton-like solution is obtained. Subsequently, through the bilinear Bäcklund transformation gained, the one-soliton-like solution is derived from a vacuum one. Furthermore, the N-soliton-like solution in the Wronskian form is constructed and verified via the Wronskian technique.

Keywords:Non-isospectral; Lax pair; Bilinear equations; N-soliton-like solution; Bäcklund transformation; Wronskian solution; Symbolic computation

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