Integrable properties for a generalized nonisospectral and variable-coefficient Korteweg-de Vries model

Xu Xiaoge; Meng XiangHua; Gao YiTian

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Integrable properties for a generalized nonisospectral and variable-coefficient Korteweg-de Vries model

Xu Xiaoge 1 *,Meng XiangHua 2,Gao YiTian 3

1.Beijing Information Science and Technology University

2.Beijing University of Posts and Telecommunications

3.Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics

*Correspondence author

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Funding: 教育部博士点基金，国家自然科学基金，973项目（No.20060006024，60772023,60372095，2005CB321901）

Opened online:22 September 2008

Accepted by: none

Citation: Xu Xiaoge,Meng XiangHua ,Gao YiTian .Integrable properties for a generalized nonisospectral and variable-coefficient Korteweg-de Vries model[OL]. [22 September 2008] http://en.paper.edu.cn/en_releasepaper/content/24249

Applicable in fluid dynamics and plasmas, a generalized variable-coefficient Korteweg-de Vries (vcKdV) equation is investigated analytically employing the Hirota bilinear method in this paper. The bilinear form for such a model is derived through a dependent variable transformation. Based on the bilinear form, the integrable properties such as the N-solitonic solution, the Bäcklund transformation and the Lax pair for the vcKdV equation are obtained. Additionally, it is shown that the bilinear Bäcklund transformation can turn into the one denoted in the original variables.

Keywords:Hirota bilinear method; Generalized nonisospectral and variable-coefficient Korteweg-de Vries equation; N-solitonic solution; Bäcklund transformation; Lax pair

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