  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.
