We introduce a nonlinear Schrödinger 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 the motion of the driven soliton with an exponentially growing amplitudes of oscillations.

我们介绍了一个非线性伪薛定ding方程（NLSE），它结合了伪刺激拉曼散射（伪SRS）术语，即具有一阶空间导数和外部电势的非保守三次方，它有助于稳定孤子以抵抗伪SRS效应。孤子的动力学通过解析和数值方法解决。孤子的准粒子近似（QPA）证明，SRS引起的孤子波数下移可以通过势力来补偿，从而产生稳定的静止孤子。考虑了三个物理上相关的电势：一个谐波振荡器（HO）陷阱，一个空间周期性的余弦形电势以及经过周期性时间调制的HO陷阱。QPA准确地预测了被捕获的脉冲（孤子）的平衡位置及其具有被捕获和自由轨迹的运动方式，并通过对底层NLSE的直接模拟来证实。在采用时间调制的HO阱的情况下，以谐振孤子的运动形式显示了参数谐振，其中振荡幅度呈指数增长。