Systems of equations of $n$-waves and nonlinear Schrödinger equations from the group-theoretical point of view

The paper is devoted to group-theoretical analysis of a system of equations of $n$-waves and a system of nonlinear Schrödinger equations. The Lie–Bäcklund algebras of these equations are fully described. These algebras are commutative, and there is a one-toone correspondence between them and the commutative Lie algebras of the conservation laws. The connection between the Lie–Bäcklund algebras of the considered systems of equations is found.