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Nonlocal symmetries and the nth finite symmetry transformation or AKNS system

Xiazhi Hao

http://orcid.org/0000-0002-4900-5107

School of Computer Science and Software Engineering, East China Normal University, Shanghai 200062, China

E-mail Address: haoxiazhi2008@163.com

Corresponding author.

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Yinping Liu

School of Computer Science and Software Engineering, East China Normal University, Shanghai 200062, China

E-mail Address: ypliu@cs.ecnu.edu.cn

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Xiaoyan Tang

School of Computer Science and Software Engineering, East China Normal University, Shanghai 200062, China

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Zhibin Li

School of Computer Science and Software Engineering, East China Normal University, Shanghai 200062, China

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, and

Wen-Xiu Ma

Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China

International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus Private Bag X2046, Mmabatho 2735, South Africa

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https://doi.org/10.1142/S0217984918503323Cited by:7 (Source: Crossref)

Abstract

In this paper, by introduction of pseudopotentials, the nonlocal symmetry is obtained for the Ablowitz–Kaup–Newell–Segur system, which is used to describe many physical phenomena in different applications. Together with some auxiliary variables, this kind of nonlocal symmetry can be localized to Lie point symmetry and the corresponding once finite symmetry transformation is calculated for both the original system and the prolonged system. Furthermore, the nth finite symmetry transformation represented in terms of determinant and exact solutions are derived.

Keywords:

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