  Dynamics of solitons is considered in an extended nonlinear Schr\"odinger
equation, including a pseudo-stimulated-Raman-scattering (pseudo-SRS) term
(scattering on damping low-frequency waves, third-order dispersion (TOD) 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 TOD. The equilibrium state
is stable for positive parameter of TOD and unstable for negative one. The
analytical solutions are verified by comparison with numerical results
