Scattering of plane waves in self-dual Yang-Mills theory

We consider the classical self-dual Yang-Mills equation in (3 + 1)-dimensional Minkowski space. We have found a new solution. It describes the scattering of n plane waves. The construction which we use is similar to the quantum inverse scattering method. We introduce a 'Monodromy matrix' (T) over cap. It acts in the direct product of the universal enveloping of SU(N) algebra and an auxiliary linear space. In order to obtain the solution of the self-dual Yang-Mills equation, we take a special matrix element of (1-(T) over cap)(-1) in the auxiliary space.