Non-trivial class of the mixed U(σ+μ)-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(σ+μ)-vector solitons with "inelastic" (changing the form without the energy loss) interaction at σ>1 and strict elastic - at σ=1. They correspond to the color complexes consisting of σ-bright and μ-dark solitons (σ+μ=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.