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' T̂. 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 - T̂)^-1 in the auxiliary space.