  Dynamics of solitons is considered in the framework of an extended nonlinear
Schr\"odinger equation (NLSE), which is derived from a Zakharov-type model for
wind-driven high-frequency (HF) surface waves in the ocean, coupled to damped
low-frequency (LF) internal waves. The drive gives rise to a convective (but
not absolute) instability in the system. The resulting NLSE includes a
pseudo-stimulated-Raman-scattering (pseudo-SRS) term, which is a spatial-domain
counterpart of the SRS term, a well-known ingredient of the temporal-domain
NLSE in optics. Analysis of the field-momentum balance and direct simulations
demonstrate that wavenumber downshift by the pseudo-SRS may be compensated by
the upshift induced by the wind traction, thus maintaining robust bright
solitons in both stationary and oscillatory forms; in particular, they are not
destroyed by the underlying convective instability. Analytical soliton
solutions are found in an approximate form and verified by numerical
simulations. Solutions for soliton pairs are obtained in the numerical form.
