Journal of Nonlinear Mathematical Physics

Volume 23, Issue 1, January 2016, Pages 92 - 107

The Ablowitz–Ladik hierarchy integrability analysis revisited: the vertex operator solution representation structure

Authors
Yarema A. Prykarpatskyy
Department of Applied Mathematics, University of Agriculture, Balicka 253c, 30-198, Krakow, Poland; Institute of Mathematics at the NAS, Kyiv, Ukraine;
Department Mathematics, Ivan Franko Pedagogical State University, Drohobych, Lviv region, Ukraine, yarpry@gmail.com
Received 12 June 2015, Accepted 24 October 2015, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2016.1135644How to use a DOI?
Keywords
the Ablowitz–Ladik hierarchy, discrete Lax type integrability, Lie-algebraic approach, vertex operator structure
Abstract

A regular gradient-holonomic approach to studying the Lax type integrability of the Ablowitz–Ladik hierarchy of nonlinear Lax type integrable discrete dynamical systems in the vertex operator representation is presented. The relationship to the Lie-algebraic integrability scheme is analyzed and the connection with the τ-function representation is discussed.

Copyright
© 2016 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
23 - 1
Pages
92 - 107
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2016.1135644How to use a DOI?
Copyright
© 2016 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  - Yarema A. Prykarpatskyy
PY  - 2021
DA  - 2021/01
TI  - The Ablowitz–Ladik hierarchy integrability analysis revisited: the vertex operator solution representation structure
JO  - Journal of Nonlinear Mathematical Physics
SP  - 92
EP  - 107
VL  - 23
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2016.1135644
DO  - https://doi.org/10.1080/14029251.2016.1135644
ID  - Prykarpatskyy2021
ER  -