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