Chvartatskyi O. Integration of Lax representations with the additional reductions.

In the thesis the relationship between two methods of the solution generating technique for nonlinear integrable systems is investigated. Namely, the relationship between the method of Darboux-Crum-Matveev differential transformations and V.O. Marchenko projection approach is considered. New generalizations of the Kadomtsev-Petviashvili hierarchy with nonlocal constraints are constructed. All main objects of the Inverse Scattering problem for the hyperbolic system of two equations are constructed in case of the degenerate scattering data. The equivalence of two approaches for the hyperbolic system of two equations is proven.