Dissipative solitons of scalar nonlinear Schroedinger equation

Numerical simulation methods have been used to analyze the evolution of a dissipative soliton solution of a scalar nonlinear Schroedinger equation with decreasing boundary conditions, taking into account damping and pumping by external boundary conditions and nonzero motion velocity. The formation of a stable breather solution, that is, a pulsating soliton with a doubling of the pulsation, is observed. (author)