On the ''color'' soliton stability

In addition to soliton solutions of the nonlinear Schroedinger equation with U(n, 0) ''color'' symmetry under the vanishing boundary conditions solutions under the nonvanishing ones are found. The energetical Q-stability investigation for both of them is reduced to the eigenvalue problem for an auxiliary matrix operator. To examine its spectrum the presence of ''color'' zero modes (i. e. generated by the ''color'' symmetry) appears rather essential. The consideration carried out permits to draw a conclusion on the applicability of the Q-theorem. With its help the stability of solitons is proved under the vanishing boundary conditions with arbitrarily chosen parameter magnitudes. Instability of solutions which are constants at both infinities is also shown for any allowable initial values