Multiple Darboux-Bäcklund transformations via truncated Painlevé expansion and Lie point symmetry approach

doi:10.1088/1674-1056/27/6/060201

Abstract

For a given truncated Painlevé expansion of an arbitrary nonlinear Painlevé integrable system, the residue with respect to the singularity manifold is known as a nonlocal symmetry, called the residual symmetry, which is proved to be localized to Lie point symmetries for suitable prolonged systems. Taking the Korteweg-de Vries equation as an example, the n-th binary Darboux-Bäcklund transformation is re-obtained by the Lie point symmetry approach accompanied by the localization of the n-fold residual symmetries.

Keywords: residue symmetry multiple Darboux-Bäcklund transformation Lie point symmetry approach

Received: 13 February 2018
Revised: 16 March 2018
Accepted manuscript online:

PACS:	02.30.Ik	(Integrable systems)
	05.45.Yv	(Solitons)

Fund:

Project supported by the National Natural Science Foundation of China (Grant Nos.11675055,11175092,and 11205092),the Program from Shanghai Knowledge Service Platform for Trustworthy Internet of Things (Grant No.ZF1213),and K C Wong Magna Fund in Ningbo University.

Corresponding Authors: Xiao-Yan Tang
E-mail: xytang@sist.ecnu.edu.cn

Cite this article:

Shuai-Jun Liu(刘帅君), Xiao-Yan Tang(唐晓艳), Sen-Yue Lou(楼森岳) Multiple Darboux-Bäcklund transformations via truncated Painlevé expansion and Lie point symmetry approach 2018 Chin. Phys. B 27 060201

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Multiple Darboux-Bäcklund transformations via truncated Painlevé expansion and Lie point symmetry approach

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