On construction of solutions of evolutionary Non Linear Schrodinger equation

In this work we present an application of a theory of vessels to solution of the evolutionary Non Liner Schrodinger (NLS) equation. The classes of functions for which the initial value problem is solvable relies on the existence of an analogue of the inverse scattering theory for the usual NLS equation. This approach is similar to the classical approach of Zackarov-Shabbath for solving of evolutionary NLS equation, but has an advantage of simpler formulas and new techniques and notions to construct solutions of the evolutionary NLS equation.