Journal of Nonlinear Mathematical Physics

Volume 19, Issue 1, March 2012, Pages 1 - 15

The AKNS Hierarchy Revisited: A Vertex Operator Approach and its Lie-Algebraic Structure

Authors
Denis Blackmore
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102-1982, USA, deblac@m.njit.edu
Anatoliy K. Prykarpatsky
Department of Mining Geodesy and Environment Engineering, AGH University of Science and Technology, Krakow 30059, Poland
Department of Economic Cybernetics, Ivan Franko Pedagogical State University, Drohobych, Lviv Region, 82100, Ukraine, pryk.anat@ua.fm, prykanat@cybergal.com
Received 22 August 2011, Accepted 23 September 2011, Available Online 20 September 2021.
DOI
https://doi.org/10.1142/S1402925112500015How to use a DOI?
Keywords
AKNS hierarchy, Lax integrability, Lie-algebraic approach, vertex operators
Abstract

A novel approach — based upon vertex operator representation — is devised to study the AKNS hierarchy. It is shown that this method reveals the remarkable properties of the AKNS hierarchy in relatively simple, rather natural and particularly effective ways. In addition, the connection of this vertex operator based approach with Lie-algebraic integrability schemes is analyzed and its relationship with τ-function representations is briefly discussed.

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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
19 - 1
Pages
1 - 15
Publication Date
2021/09/20
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925112500015How to use a DOI?
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/).

Cite this article

TY  - JOUR
AU  - Denis Blackmore
AU  - Anatoliy K. Prykarpatsky
PY  - 2021
DA  - 2021/09/20
TI  - The AKNS Hierarchy Revisited: A Vertex Operator Approach and its Lie-Algebraic Structure
JO  - Journal of Nonlinear Mathematical Physics
SP  - 1
EP  - 15
VL  - 19
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925112500015
DO  - https://doi.org/10.1142/S1402925112500015
ID  - Blackmore2021
ER  -