Liouville's theorem and the inverse scattering method

On the base of Liouville's theorem, an approach to the integration of the Zakharov–Shabat equations is developed. It arises as a synthesis of ideas of the “finite-gape” integration, the matrix Riemann problem method and the theory of isomonodromic deformations. With the help of this scheme the “dressing procedure” for the Bullough–Dodd equation is obtained.