Journal of Nonlinear Mathematical Physics

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Volume 25, Issue 2, March 2018, Pages 324 - 350

Pseudo-Hermitian Reduction of a Generalized Heisenberg Ferromagnet Equation. I. Auxiliary System and Fundamental Properties

Authors
A. B. Yanovski
Department of Mathematics & Applied Mathematics, University of Cape Town, Rondebosch 7700, Cape Town, South Africa,Alexandar.Ianovsky@uct.ac.za
T. I. Valchev
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., 1113 Sofia, Bulgaria,tiv@math.bas.bg
Received 8 October 2017, Accepted 9 January 2018, Available Online 6 January 2021.
DOI
10.1080/14029251.2018.1452676How to use a DOI?
Keywords
Lax representation; gauge-equivalent equations; recursion operators; reductions
Abstract

We consider an auxiliary spectral problem originally introduced by Gerdjikov, Mikhailov and Valchev (GMV system) and its modification called pseudo-Hermitian reduction which is extensively studied here for the first time. We describe the integrable hierarchies of both systems in a parallel way and construct recursion operators. Using the concept of gauge equivalence, we construct expansions over the eigenfunctions of recursion operators. This permits us to obtain the expansions for both GMV systems with arbitrary constant asymptotic values of the potential functions in the auxiliary linear problems.

Copyright
© 2018 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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<Previous Article In Issue
Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
25 - 2
Pages
324 - 350
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2018.1452676How to use a DOI?
Copyright
© 2018 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

risenwbib
TY  - JOUR
AU  - A. B. Yanovski
AU  - T. I. Valchev
PY  - 2021
DA  - 2021/01/06
TI  - Pseudo-Hermitian Reduction of a Generalized Heisenberg Ferromagnet Equation. I. Auxiliary System and Fundamental Properties
JO  - Journal of Nonlinear Mathematical Physics
SP  - 324
EP  - 350
VL  - 25
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2018.1452676
DO  - 10.1080/14029251.2018.1452676
ID  - Yanovski2021
ER  -