Backlund-Transformation-Related Recursion Operators: Application to the Self-Dual Yang-Mills Equation
Mathematical Physics
2023-06-22 v3 math.MP
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-Backlund 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.
Cite
@article{arxiv.0809.0981,
title = {Backlund-Transformation-Related Recursion Operators: Application to the Self-Dual Yang-Mills Equation},
author = {C. J. Papachristou and B. Kent Harrison},
journal= {arXiv preprint arXiv:0809.0981},
year = {2023}
}
Comments
16 pages; minor correction; final, published version