Functional Representation of the Negative AKNS Hierarchy

DOI

10.1142/S1402925112500222How to use a DOI?

Keywords

AKNS hierarchy; negative flows; functional representation; Miwa's shifts; conservation laws; dark solitons; Landau–Lifshitz hierarchy

Abstract

This paper is devoted to the negative flows of the AKNS hierarchy. The main result of this work is the functional representation of the extended AKNS hierarchy, composed of both positive (classical) and negative flows. We derive a finite set of functional equations, constructed by means of the Miwa's shifts, which contains all equations of the hierarchy. Using the obtained functional representation we convert the nonlocal equations of the negative subhierarchy into local systems of higher order, derive the generating function of the conservation laws and the N-dark-soliton solutions for the extended AKNS hierarchy. As an additional result we obtain the functional representation of the Landau–Lifshitz hierarchy.

Copyright

© 2012 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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TY  - JOUR
AU  - V. E. Vekslerchik
PY  - 2012
DA  - 2012/09/20
TI  - Functional Representation of the Negative AKNS Hierarchy
JO  - Journal of Nonlinear Mathematical Physics
SP  - 353
EP  - 372
VL  - 19
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925112500222
DO  - 10.1142/S1402925112500222
ID  - Vekslerchik2012
ER  -