Journal of Nonlinear Mathematical Physics

Volume 22, Issue 3, June 2015, Pages 321 - 341

Continuous Correspondence of Conservation Laws of the Semi-discrete AKNS System

Authors
Wei Fu*
Department of Mathematics, Shanghai University Shanghai, 200444, People's Republic of China
Zhijun Qiao
Department of Mathematics, The University of Texas-Rio Grande Valley Edinburg, TX 78541, United States of America
Junwei Sun
Department of Mathematics, The University of Texas at Arlington Arlington, TX 76019, United States of America
Da-jun Zhang
Department of Mathematics, Shanghai University Shanghai, 200444, People's Republic of China.djzhang@staff.shu.edu.cn
*

Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom

Corresponding author.
Corresponding Author
Da-jun Zhang
Received 24 September 2014, Accepted 6 March 2015, Available Online 6 January 2021.
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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
22 - 3
Pages
321 - 341
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2015.1056612How to use a DOI?
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  -