Self-similar soliton-like solutions to a system of two nonlinear Schr$\stackrel{..}{o}$dinger-type equations (NSE) for various sets of coefficients have been studied theoretically and numerically. In the case of equality of the corresponding coefficients in the two equations of the system, a family of solitons of a new class with complex amplitude modulation has been found. The existence and uniqueness theorem for the NSE system has been proved and the related finite-difference scheme investigated.
Department of Radiophysics, Faculty of Physics, Moscow State University, Leninskie Gory, Moscow, 119992, Russia
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