The Wronskian technique for nonlinear evolution equations

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

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.

Keywords: nonlinear evolution equations Wronskian determinant Young diagram

Received: 07 March 2015
Revised: 29 August 2015
Accepted manuscript online:

PACS:	05.45.Yv	(Solitons)
	02.30.Ik	(Integrable systems)
	02.30.Jr	(Partial differential equations)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 51379033, 51522902, 51579040, J1103110, and 11201048).

Corresponding Authors: Jian-Jun Cheng
E-mail: chengjianjun0355@126.com

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

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