Reduction of the Symmetries of the Self-dual Yang-Mills Equation

Abstract

We know that the self-dual Yang-Mills (SDYM) equation has infinitely manysymmetries, and these symmtries constitute an infinite dimensional Lie algebra.This property is commonly shared by almost all the 1+l-dimensional integrableevolution equations (soliton equations), and has become a very important criterion ofintegrability for the evolution equations. So in a sense the SDYM equation is integr-able. In recent years people have found that some typical soliton equations, such as