Non-trivial class of the mixed U(σ+μ)-vector solitons

Details Non-trivial class of the mixed U(σ+μ)-vector solitons Non-trivial class of the mixed U(σ+μ)-vector solitons

2002-09-04

arxiv.org/abs/nlin/0209012v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

9 pages, LaTex or MiKTex, Submitted to Pis'ma v ZhETF

Scientific paper

10.1134/1.1528692

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.

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