论文标题
伪拉曼项的相互作用和非线性schroedinger方程中的诱捕电势
Interplay of the pseudo-Raman term and trapping potentials in the nonlinear Schroedinger equation
论文作者
论文摘要
我们介绍了一个非线性schroedinger方程（NLSE），该方程将伪刺激的 - 拉曼 - 散布（伪SRS）术语结合在一起，即非保守的非保守性立方衍生物和第一个空间衍生物，以及外部电位，有助于稳定抗溶质剂对PSEUDO-SRS的效应。孤子的动力学是通过分析和数值方法来解决的。孤子的准粒子近似（QPA）表明，SRS诱导的孤子波数的降档可以通过潜在的力来补偿，从而产生稳定的固定孤子。考虑了三个与物理相关的电位：谐波振荡器（HO）陷阱，空间周期性的助势和HO陷阱受到周期性时间调制。 QPA准确地预测了被困脉冲（孤子）的平衡位置及其具有捕获和游离轨迹的运动状态，并通过直接模拟基础NLSE进行了证实。在时间调节的HO陷阱的情况下，以驱动孤子的运动形式证明了参数共振，并具有指数增长的振荡振幅。
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.
