Fedorov S, Michaelis D, Peschel U, Etrich C, Skryabin D V, Rosanov N, Lederer F
Institute for Laser Physics, Vavilov State Optical Institute, Birzhevaya line 12, 199034 St. Petersburg, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Sep;64(3 Pt 2):036610. doi: 10.1103/PhysRevE.64.036610. Epub 2001 Aug 29.
We study the dynamics of cavity solitons under the influence of spatial inhomogeneities and derive generalized equations of motions. For perturbations large compared to the soliton size we find the modulus of the soliton velocity to be proportional to the gradient of the respective perturbation and that the proportionality coefficient changes sign when the soliton peak power drives the cavity beyond the resonance. For short scale perturbations solitons may be trapped at the extrema of the inhomogeneities. Shape and stability of these trapped solitons can be quasianalytically described by means of a perturbation theory. If both types of perturbations act solitons are either trapped or move depending on the strength of the respective perturbation. In the framework of a quasiparticle approach this dynamics is governed by a differential equation that holds for particle motion in a strongly viscous fluid under the action of a constant and harmonically varying force. We also show that in addition to acquiring a velocity the very existence conditions of the solitons (hysteresis curve) are affected by both kinds of perturbations. We find good quantitative agreement between our analytical results and numerical findings, which were obtained for a two wave interaction in a cavity filled with a quadratically nonlinear material.
我们研究了空间不均匀性影响下的腔孤子动力学，并推导了广义运动方程。对于比孤子尺寸大的微扰，我们发现孤子速度的模与相应微扰的梯度成正比，并且当孤子峰值功率使腔超过共振时，比例系数会改变符号。对于短尺度微扰，孤子可能被困在不均匀性的极值处。这些被困孤子的形状和稳定性可以通过微扰理论进行准解析描述。如果两种类型的微扰都起作用，孤子会根据各自微扰的强度被捕获或移动。在准粒子方法的框架下，这种动力学由一个微分方程支配，该方程适用于在恒定和简谐变化力作用下强粘性流体中的粒子运动。我们还表明，除了获得速度外，孤子的存在条件（滞后曲线）也受到这两种微扰的影响。我们发现我们的解析结果与数值结果之间有很好的定量一致性，数值结果是针对在充满二次非线性材料的腔中的两波相互作用获得的。
