Painlevé integrability of generalized fifth-order KdV equation with variable coefficients: Exact solutions and their interactions

doi:10.1088/1674-1056/22/5/050203

中国物理B ›› 2013, Vol. 22 ›› Issue (5): 50203-050203.doi: 10.1088/1674-1056/22/5/050203

Painlevé integrability of generalized fifth-order KdV equation with variable coefficients: Exact solutions and their interactions

徐桂琼

Department of Information Management, College of Management, Shanghai University, Shanghai 200444, China

收稿日期:2012-11-21 修回日期:2013-01-05 出版日期:2013-04-01 发布日期:2013-04-01
基金资助:
Projects supported by the National Natural Science Foundation of China (Grant Nos. 11201290 and 71103118).

Painlevé integrability of generalized fifth-order KdV equation with variable coefficients: Exact solutions and their interactions

Xu Gui-Qiong (徐桂琼)

Department of Information Management, College of Management, Shanghai University, Shanghai 200444, China

Received:2012-11-21 Revised:2013-01-05 Online:2013-04-01 Published:2013-04-01
Contact: Xu Gui-Qiong E-mail:xugq@staff.shu.edu.cn
Supported by:
Projects supported by the National Natural Science Foundation of China (Grant Nos. 11201290 and 71103118).

摘要/Abstract

摘要： By means of singularity structure analysis, the integrability of a generalized fifth-order KdV equation is investigated. It is proven that this equation passes the Painlevé test for integrability only for three distinct cases. Moreover, the multi-soliton solutions are presented for this equation under three sets of integrable conditions. Finally, by selecting appropriate parameters, we analyze the evolution of two solitons, which is especially interesting as it may describe the overtaking and the head-on collisions of solitary waves of different shapes and different types.

关键词: generalized fifth-order KdV equation, Painlevé, integrability, soliton solution, symbolic computation

Abstract: By means of singularity structure analysis, the integrability of a generalized fifth-order KdV equation is investigated. It is proven that this equation passes the Painlevé test for integrability only for three distinct cases. Moreover, the multi-soliton solutions are presented for this equation under three sets of integrable conditions. Finally, by selecting appropriate parameters, we analyze the evolution of two solitons, which is especially interesting as it may describe the overtaking and the head-on collisions of solitary waves of different shapes and different types.

Key words: generalized fifth-order KdV equation, Painlevé, integrability, soliton solution, symbolic computation

中图分类号: (Integrable systems)

02.30.Ik

05.45.Yv (Solitons) 02.30.Jr (Partial differential equations)

徐桂琼. Painlevé integrability of generalized fifth-order KdV equation with variable coefficients: Exact solutions and their interactions[J]. 中国物理B, 2013, 22(5): 50203-050203.

Xu Gui-Qiong (徐桂琼). Painlevé integrability of generalized fifth-order KdV equation with variable coefficients: Exact solutions and their interactions[J]. Chin. Phys. B, 2013, 22(5): 50203-050203.

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Painlevé integrability of generalized fifth-order KdV equation with variable coefficients: Exact solutions and their interactions

Painlevé integrability of generalized fifth-order KdV equation with variable coefficients: Exact solutions and their interactions

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