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Dynamics of solitons is considered in an extended nonlinear Schrodinger equation, including a pseudo-stimulated-Raman-scattering (pseudo-SRS) term (scattering on damping low-frequency waves, nonlinear dispersion and inhomogeneity of the spatial second-order dispersion (SOD). It is shown that wave-number downshift by the pseudo-SRS may be compensated by upshift provided by spatially increasing SOD with taking into account nonlinear dispersion. The equilibrium state is stable for negative parameter of nonlinear dispersion and unstable for positive one. The analytical solutions are verified by comparison with numerical results

Soliton in an extended nonlinear Schrödinger equation with stimulated scattering on damping low-frequency waves and nonlinear dispersion