  We introduce a nonlinear Schroedinger equation (NLSE) which combines the
pseudo-stimulated-Raman-scattering (pseudo-SRS) term, i.e., a non-conservative
cubic one with the first spatial derivative, and an external potential, which
helps to stabilize solitons against the pseudo-SRS effect. Dynamics of solitons
is addressed by means of analytical and numerical methods. The quasi-particle
approximation (QPA) for the solitons demonstrates that the SRS-induced
downshift of the soliton's wavenumber may be compensated by a potential force,
producing a stable stationary soliton. Three physically relevant potentials are
considered: a harmonic-oscillator (HO) trap, a spatially periodic cosinusoidal
potential, and the HO trap subjected to periodic temporal modulation. Both
equilibrium positions of trapped pulses (solitons) and their regimes of motion
with trapped and free trajectories are accurately predicted by the QPA and
corroborated by direct simulations of the underlying NLSE. In the case of the
time-modulated HO trap, a parametric resonance is demonstrated, in the form of
motion of the driven soliton with an exponentially growing amplitude of
oscillations.
