Journal of Nonlinear Mathematical Physics

Volume 24, Issue Supplement 1, December 2017, Pages 18 - 35

Symmetry Constraint of the Differential-difference KP Hierarchy and a Second Discretization of the ZS-AKNS System

Authors
Kui Chen, Xiao Deng, Da-jun Zhang*
Department of Mathematics, Shanghai University, Shanghai 200444, People’s Republic of China
*Corresponding author. djzhang@staff.shu.edu.cn
Corresponding Author
Da-jun Zhang
Received 22 July 2017, Accepted 28 August 2017, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2017.1418051How to use a DOI?
Keywords
differential-difference KP hierarchy, squared-eigenfunction, symmetry, symmetry constraint, ZSAKNS spectral problem, semi-discrete AKNS hierarchies
Abstract

In this paper we construct a squared-eigenfunction symmetry of the scalar differential-difference KP hierarchy. Through a constraint of the symmetry, Lax triad of the differential-difference KP hierarchy is reduced to a known discrete spectral problem and a semidiscrete AKNS hierarchy. The discrete spectral problem corresponds to a bidirectional discretization of the derivatives φ1, x and φ2, x in the ZS-AKNS spectral problem and therefore it is a discretization of the later. The discrete spectral problem is also known as a Darboux transformation of the ZS-AKNS spectral problem. Isospectral and nonisospectral flows derived from the spectral problem compose a Lie algebra. Infinitely many symmetries of the nonisospectral hierarchy are obtained. By considering infinite dimensional subalgebras of the algebra and continuum limit of recursion operator, three semi-discrete AKNS hierarchies are constructed.

Copyright
© 2017 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
24 - Supplement 1
Pages
18 - 35
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2017.1418051How to use a DOI?
Copyright
© 2017 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Kui Chen
AU  - Xiao Deng
AU  - Da-jun Zhang
PY  - 2021
DA  - 2021/01
TI  - Symmetry Constraint of the Differential-difference KP Hierarchy and a Second Discretization of the ZS-AKNS System
JO  - Journal of Nonlinear Mathematical Physics
SP  - 18
EP  - 35
VL  - 24
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2017.1418051
DO  - https://doi.org/10.1080/14029251.2017.1418051
ID  - Chen2021
ER  -