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Dynamics of solitons is considered in the framework of the extended nonlinearSchrodinger equation (NLSE), which is derived from a system of Zakharov's typefor the interaction between high- and low-frequency (HF and LF) waves, in whichthe LF field is subject to diffusive damping. The model may apply to thepropagation of HF waves in plasmas. The resulting NLSE includes apseudo-stimulated-Raman-scattering (PSRS) term, i.e., a spatial-domaincounterpart of the SRS term which is well known as an ingredient of thetemporal-domain NLSE in optics. Also included is inhomogeneity of the spatialsecond-order diffraction (SOD). It is shown that the wavenumber downshift ofsolitons, caused by the PSRS, may be compensated by an upshift provided by theSOD whose coefficient is a linear function of the coordinate. An analyticalsolution for solitons is obtained in an approximate form. Analytical andnumerical results agree well, including the predicted balance between the PSRSand the linearly inhomogeneous SOD.

Soliton dynamics in an extended nonlinear Schrodinger equation with a spatial counterpart of the stimulated Raman scattering