Liouville's theorem and the method of the inverse problem

Abstract

An approach to the investigation of the Zakharov-Shabat equations is developed. This approach is based on a classical theorem of Liouville and is the synthesis of “finite-zone” integration, the matrix Riemann problem method and the theory of isomonodromy deformations of differential equations. The effectiveness of the proposed scheme is demonstrated by developing “dressing procedures” for the Bullough-Dodd equation.