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

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 proble...

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Bibliographic Details
Published inJournal of nonlinear mathematical physics Vol. 22; no. 3; pp. 321 - 341
Main Authors Fu, Wei, Qiao, Zhijun, Sun, Junwei, Zhang, Da-jun
Format Journal Article
LanguageEnglish
Published Dordrecht Taylor & Francis 01.01.2015
Springer Netherlands
Springer Nature B.V
Subjects
Combinatorial analysis
Conservation laws
continuum limits
Lax pairs
Research Article
semi-discrete AKNS hierarchy
39A99
semi-discrete AKNS hierarchy
conservation laws
37K05
35Q55
continuum limits
35Q51
Lax pairs
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Summary: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.
ISSN:1402-9251
1776-0852
1776-0852
DOI:10.1080/14029251.2015.1056612