Symmetries and reduced systems of equations for three-boson and four-boson interactions

Abstract

A reduced system of equations is found for three-boson and four-boson interactions. The invariants and surfaces in the space of parameters connected with these systems are constructed. It is shown that at these surfaces the eigenvectors can be presented in power form. The connection between the ansatz and polynomial extensions of Lie algebras is briefly discussed. The computational procedures corresponding to the original equations and the method of polynomial algebras are compared.