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Dynamics of solitons is considered in the framework of an extended nonlinearSchrodinger equation (NLSE), which is derived from a system of the Zakharov'stype for the interaction between high- and low-frequency (HF and LF) waves. Theresulting NLSE includes a pseudo-stimulated-Raman-scattering (pseudo-SRS) term,i.e., a spatial-domain counterpart of the SRS term, which is a known ingredientof the temporal-domain NLSE in optics. Also included is inhomogeneity of thespatial second-order dispersion (SOD) and linear losses of HF waves. It isshown that wavenumber downshift by the pseudo-SRS may be compensated by upshiftprovided by SOD whose local strength is an exponentially decaying function ofthe coordinate. An analytical soliton solution with a permanent shape is foundin an approximate form, and is verified by comparison with numerical results

Damped solitons in an extended nonlinear Schrodinger equation with a spatial stimulated Raman scattering and decreasing dispersion