Hamiltonian formalism in a problem of 3-th waves hierarchy

Abstract

By the method of discrete transformation equations of 3-th wave hierarchy are constructed. We present in explicit form two Poisson structures, which allow to construct Hamiltonian operator consequent application of which leads to all equations of this hierarchy. For calculations it will be necessary results of previous paper \cite{1}, which for convenience of the reader we present in corresponding place of the text. The obtained formulae are checked by independent calculations.