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

Details Backlund-Transformation-Related Recursion Operators: Application to the Self-Dual Yang-Mills Equation Backlund-Transformation-Related Recursion Operators: Application to the Self-Dual Yang-Mills Equation

2008-09-05

arxiv.org/abs/0809.0981v2

Physics

Mathematical Physics

16 pages. Minor corrections, updated bibliography

Scientific paper

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.

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