Equations of 3-th waves hierarchy

Abstract

By the method of discrete transformation equations of 3-th wave hierarchy are constructed. The main difference compare with the systems connected with $A_1$ algebra consists in a fact that in $A_2$ case there are two different systems of equations of the same degree (the maximal derivatives with respect to space coordinate). In the present paper we construct only system of equations of zero, first and second degree. At this moment the general method for solution of this problem (the type of canonical Hamiltonian operators) is unknown for the author and our direct calculationsare sufficiently combersome.