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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Published in | Journal of nonlinear mathematical physics Vol. 22; no. 3; pp. 321 - 341 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Dordrecht
Taylor & Francis
01.01.2015
Springer Netherlands Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 1402-9251 1776-0852 1776-0852 |
DOI: | 10.1080/14029251.2015.1056612 |