Journal of Nonlinear Mathematical Physics

Volume 17, Issue 1, March 2013, Pages 35 - 49

Bäcklund-Transformation-Related Recursion Operators: Application to the Self-Dual Yang–Mills Equation

Authors
C. J. Papachristou
Department of Physical Sciences, Naval Academy of Greece, Piraeus 18539, Greece, papachristou@snd.edu.gr
B. Kent Harrison
Department of Physics and Astronomy, Brigham Young University, Provo, UT 84602, USA, bkentharrison@comcast.net, bkh@byu.edu
Received 13 February 2009, Accepted 15 June 2009, Available Online 7 January 2021.
DOI
https://doi.org/10.1142/S1402925110000581How to use a DOI?
Keywords
Bäcklund transformations, recursion operators, self-dual Yang–Mills equation
Abstract

By using the self-dual Yang–Mills (SDYM) equation as an example, we study a method for relating symmetries and recursion operators of two partial differential equations connected to each other by a non-auto-Bäcklund transformation. We prove the Lie-algebra isomorphism between the symmetries of the SDYM equation and those of the potential SDYM (PSDYM) equation, and we describe the construction of the recursion operators for these two systems. Using certain known aspects of the PSDYM symmetry algebra, we draw conclusions regarding the Lie algebraic structure of the “potential symmetries” of the SDYM equation.

Copyright
© 2010 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
17 - 1
Pages
35 - 49
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925110000581How to use a DOI?
Copyright
© 2010 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  - C. J. Papachristou
AU  - B. Kent Harrison
PY  - 2021
DA  - 2021/01
TI  - Bäcklund-Transformation-Related Recursion Operators: Application to the Self-Dual Yang–Mills Equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 35
EP  - 49
VL  - 17
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925110000581
DO  - https://doi.org/10.1142/S1402925110000581
ID  - Papachristou2021
ER  -