平顶-气泡矢量孤子的动力学
Dynamics of Flat-Top--Bubble Vector Solitons
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中文总结 AI 辅助
本文研究二分量平顶-气泡矢量孤子动力学，用变分近似和数值模拟揭示其自诱导复合束缚机制，预测并验证了弱振荡频率特性及部分逃逸的扰动尺度。
中文摘要 AI 辅助
我们采用变分近似和数值模拟研究了二分量平顶-气泡矢量孤子的动力学。该系统由带分量间排斥耦合的耦合三次-五次非线性薛定谔方程描述。我们引入了一种自诱导机制：局域平顶孤子（FTS）在第二分量中产生密度气泡，该局域密度作为背景场的排斥势，形成复合束缚态。采用背景扣除公式和归一化超高斯分布，得到了分量中心的集体坐标方程以及它们相对间距的有效相互作用势。该势在整体位移范围内形成近似三角形的束缚势阱，在最小值附近则是平滑的局部抛物线形。因此，变分近似预测在小振荡区域内，谐波内部振荡的频率与振幅无关。实时模拟验证了这种弱扰动行为，变分频率与数值频率吻合良好。对于强相位印记，将精确的扰动能量等于变分束缚深度，可预测部分FTS逃逸起始的扰动尺度K_escape。实时模拟支持该预测：低于此尺度，复合结构几乎保持完整；高于此尺度，局域分量的相当一部分会离开气泡。
英文摘要
We investigate the dynamics of two-component flat-top--bubble vector solitons using a variational approximation and numerical simulations. The system is described by coupled cubic-quintic nonlinear Schrödinger equations with repulsive intercomponent coupling. We introduce a self-induced mechanism in which a localized flat-top soliton (FTS) generates a density bubble in a second component: the localized density acts as a repulsive potential for the background field, creating a composite bound state. A background-subtracted formulation and normalized super-Gaussian profiles yield collective-coordinate equations for the component centers and an effective interaction potential for their relative separation. The potential forms a binding well that is nearly triangular over its global displacement range but smooth and locally parabolic near its minimum. The variational approximation consequently predicts harmonic internal oscillations whose frequency is independent of amplitude in the small-oscillation regime. Real-time simulations verify this weak-kick behavior with good agreement between the variational and numerical frequencies. For strong phase imprints, equating the exact kick energy to the variational binding depth predicts a kick scale \(K_{\mathrm{escape}}\) for the onset of partial FTS escape. Real-time simulations support this prediction: below this scale, the composite remains nearly intact, whereas above it, a substantial fraction of the localized component leaves the bubble.
