Continuous Correspondence of Conservation Laws of the Semi-discrete AKNS System
Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom
- DOI
- 10.1080/14029251.2015.1056612How to use a DOI?
- Keywords
- semi-discrete AKNS hierarchy; Lax pairs; conservation laws; continuum limits
- Abstract
In this paper we investigate the semi-discrete Ablowitz–Kaup–Newell–Segur (sdAKNS) hierarchy, and specifically their Lax pairs and infinitely many conservation laws, as well as the corresponding continuum limits. The infinitely many conserved densities derived from the Ablowitz-Ladik spectral problem are trivial, in the sense that all of them are shown to reduce to the first conserved density of the AKNS hierarchy in the continuum limit. We derive new and nontrivial infinitely many conservation laws for the sdAKNS hierarchy, and also the explicit combinatorial relations between the known conservation laws and our new ones. By performing a uniform continuum limit, the new conservation laws of the sdAKNS system are then matched with their counterparts of the continuous AKNS system.
- Copyright
- © 2015 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 - Wei Fu AU - Zhijun Qiao AU - Junwei Sun AU - Da-jun Zhang PY - 2021 DA - 2021/01/06 TI - Continuous Correspondence of Conservation Laws of the Semi-discrete AKNS System JO - Journal of Nonlinear Mathematical Physics SP - 321 EP - 341 VL - 22 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2015.1056612 DO - 10.1080/14029251.2015.1056612 ID - Fu2021 ER -