Self-Dual Yang–Mills Equations and Integrable Reductions

Abstract

The self-dual Yang-Mills equations and their corresponding Lax pair (or linear system) in R4, endowed with Euclidean metric or the pseudo-Euclidean metric of signature (2, 2), have integrable reductions under subgroups of their invariance group. The general method is reviewed and generalized to Yang-Mills fields with values in Lie superalgebras. An example of such reductions is presented.