Bäcklund-Transformation-Related Recursion Operators: Application to the Self-Dual Yang–Mills Equation
- https://doi.org/10.1142/S1402925110000581How to use a DOI?
- Bäcklund transformations, recursion operators, self-dual Yang–Mills equation
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.
- © 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 -