Some exact solutions of a system of nonlinear Schrödinger equations in three-dimensional space

Most general interaction terms are constructed which reduce the symmetry group of the nonrelativistic Schrödinger equations to its one-parameter subgroups. Ansatze of invariant solutions of the Galilei-invariant Schrödinger equations and corresponding systems of reduced equations in terms of invariant variables are found. Some exact solutions of the system of nonlinear Schrödinger equations are obtained in three spatial dimensions for the case of the generalised Hubbard model.