Non-trivial class of the mixed U(\sigma+\mu)-vector solitons

Abstract

There has been found an exact solution of the mixed problem for Shrodinger's compact U(m)-vector nonlinear model with an arbitrary sign of the coupling constant. It is shown, that in case of m>2 there is a new class of solutions - mixed U(\sigma+\mu)-vector solitons with "inelastic" (changing the form without the energy loss) interaction at \sigma>1 and strict elastic - at \sigma=1. They correspond to the color complexes consisting of \sigma-bright and \mu-dark solitons (\sigma+\mu=m) and they can exist both in self-focusing and defocusing medias. The universal N-soliton formula for the attraction and repulsion cases has been obtained by the method of Hirota for the first time.