Matrix Piemann Problem of the AKNS Equation

Abstract

The AKNS equation is reformulated by means of the matrix Riemann problem. The projection operator arising for solving the Riemann problem is connected to the scattering data. By this fact we can completely separate the procedure for solving the problem to the determination of projection operator and to the regular problem consisting only with continuous scattering data. As an application of this we construct the way of potential proliferation.