Symmetry Constraint of the Differential-difference KP Hierarchy and a Second Discretization of the ZS-AKNS System
- DOI
- 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/).
Cite this article
TY - JOUR AU - Kui Chen AU - Xiao Deng AU - Da-jun Zhang PY - 2021 DA - 2021/01/06 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 - 10.1080/14029251.2017.1418051 ID - Chen2021 ER -