标题： 相互作用腔孤子的动力学 显示英文标题

标题： Dynamics of interacting cavity solitons

摘要： 我们推导了Kerr孤子在双波形中的运动方程。 最近在微谐振器中的实验研究了多孤子波形中各种相互作用效应，包括碰撞以及孤子分子和晶体的形成。 在这里，我们分析了由于孤子尾部重叠非线性与与打破平移对称性相关的全局孤子变量耦合而产生的有效相互作用。 根据孤子尾部的衰减是单调还是振荡，这种相互作用要么完全是排斥的，要么在吸引和排斥之间交替。 在后一种情况下，有效动力系统的稳定固定点表示稳定的孤子分子配置，但随着孤子间距离的增加，相互作用的指数减弱可能阻止分子在实验可访问的时间尺度内形成。 我们的理论在大距离极限下变得渐近精确，并且我们通过从波动方程的直接数值解中提取的孤子轨迹验证了理论计算。 显示英文摘要

摘要： We derive the equations governing the motion of Kerr solitons in pair waveforms. Recent experiments in microresonators have studied a variety of interaction effects in multisoliton waveforms, including collisions and formation of soliton molecules and crystals. Here we analyze the effective interaction that arises from the coupling of soliton-tail overlap nonlinearity with global soliton variables associated with the breaking of translation symmetry. The interaction is either purely repulsive, or alternates between attraction and repulsion, according to whether the decay of soliton tails is monotone or oscillatory. In the latter case, stable fixed points of the effective dynamical system signify stable soliton molecule configuration, but the exponential weakening of the interaction with increasing inter-soliton separation may prevent the molecule from forming in experimentally accessible time scales. Our theory becomes asymptotically exact in the large-separation limit, and we verify the theoretical calculations using soliton trajectories extracted from direct numerical solutions of the wave equation.