ИСТИНА

We describe a scheme for constructing all soliton equations of parabolic type in two-dimensional spacetime (including Korteweg-de Vries equation, the nonlinear Schroediner equation, the Boussinesq equation and their modifications and hierarchies) and all of their local holomorphic solution from scattering data that are formal matrix-valued Laurent series. As an application, we prove that every local holomorphic solution can be extended analytically to a global meromorphic function of the space variable.