The Wronskian technique for nonlinear evolution equations

doi:10.1088/1674-1056/25/1/010506

中国物理B ›› 2016, Vol. 25 ›› Issue (1): 10506-010506.doi: 10.1088/1674-1056/25/1/010506

The Wronskian technique for nonlinear evolution equations

Jian-Jun Cheng(成建军) and Hong-Qing Zhang(张鸿庆)

1. School of Mechano-Electronic Engineering, Xidian University, Xi'an 710071, China;
2. Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China

收稿日期:2015-03-07 修回日期:2015-08-29 出版日期:2016-01-05 发布日期:2016-01-05
通讯作者: Jian-Jun Cheng E-mail:chengjianjun0355@126.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 51379033, 51522902, 51579040, J1103110, and 11201048).

The Wronskian technique for nonlinear evolution equations

Jian-Jun Cheng(成建军)¹ and Hong-Qing Zhang(张鸿庆)²

1. School of Mechano-Electronic Engineering, Xidian University, Xi'an 710071, China;
2. Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China

Received:2015-03-07 Revised:2015-08-29 Online:2016-01-05 Published:2016-01-05
Contact: Jian-Jun Cheng E-mail:chengjianjun0355@126.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 51379033, 51522902, 51579040, J1103110, and 11201048).

摘要/Abstract

摘要： The investigation of the exact traveling wave solutions to the nonlinear evolution equations plays an important role in the study of nonlinear physical phenomena. To understand the mechanisms of those physical phenomena, it is necessary to explore their solutions and properties. The Wronskian technique is a powerful tool to construct multi-soliton solutions for many nonlinear evolution equations possessing Hirota bilinear forms. In the process of utilizing the Wronskian technique, the main difficulty lies in the construction of a system of linear differential conditions, which is not unique. In this paper, we give a universal method to construct a system of linear differential conditions.

关键词: nonlinear evolution equations, Wronskian determinant, Young diagram

Abstract: The investigation of the exact traveling wave solutions to the nonlinear evolution equations plays an important role in the study of nonlinear physical phenomena. To understand the mechanisms of those physical phenomena, it is necessary to explore their solutions and properties. The Wronskian technique is a powerful tool to construct multi-soliton solutions for many nonlinear evolution equations possessing Hirota bilinear forms. In the process of utilizing the Wronskian technique, the main difficulty lies in the construction of a system of linear differential conditions, which is not unique. In this paper, we give a universal method to construct a system of linear differential conditions.

Key words: nonlinear evolution equations, Wronskian determinant, Young diagram

中图分类号: (Solitons)

05.45.Yv

02.30.Ik (Integrable systems) 02.30.Jr (Partial differential equations)

成建军, 张鸿庆. The Wronskian technique for nonlinear evolution equations[J]. 中国物理B, 2016, 25(1): 10506-010506.

Jian-Jun Cheng(成建军) and Hong-Qing Zhang(张鸿庆). The Wronskian technique for nonlinear evolution equations[J]. Chin. Phys. B, 2016, 25(1): 10506-010506.

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The Wronskian technique for nonlinear evolution equations

The Wronskian technique for nonlinear evolution equations

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