色散介质中的伽利略变换孤子和超连续谱的产生
Galilean-transformed solitons and supercontinuum generation in dispersive media
摘要：
伽利略变换是一种连接动力系统坐标的通用运算，这些坐标以恒定速度相对于彼此运动。在普适非线性薛定谔方程（NLSE）的精确解的背景下，将伽利略速度（GV）引入脉冲涉及频率偏移以满足波动方程的对称性。因此，伽利略变换被认为不适用于非线性色散介质中的波群。在本文中，我们证明了在一个波槽产生的伽利略变换包络和游隼孤子显示出明显的变化，从各自的纯动力学在水面上。偏差的类型取决于GV的符号，并且可以通过修改的NLSE或欧拉方程来捕获。此外，我们还证明了正的伽利略平移包络孤子脉冲具有自调制特性。虽然指定的GS和波陡值加快多孤子动力学，这种高阶相干波的强聚焦不可避免地导致超连续波的产生，作为孤子裂变的结果。我们预计，同类的实验和数值研究可能会在其他色散波导的非线性。
英文摘要：
The Galilean transformation is a universal operation connecting the coordinates of a dynamical system, which move relative to each other with a constant speed. In the context of exact solutions of the universal nonlinear Schrödinger equation (NLSE), inducing a Galilean velocity (GV) to the pulse involves a frequency shift to satisfy the symmetry of the wave equation. As such, the Galilean transformation has been deemed to be not applicable to wave groups in nonlinear dispersive media. In this paper, we demonstrate that in a wave tank generated Galilean transformed envelope and Peregrine solitons show clear variations from their respective pure dynamics on the water surface. The type of deviations depends on the sign of the GV and can be captured by the modified NLSE or the Euler equations. Moreover, we show that positive Galilean-translated envelope soliton pulses exhibit self-modulation. While designated GS and wave steepness values expedite multi-soliton dynamics, the strong focusing of such higher-order coherent waves inevitably lead to the generation of supercontinua as a result of soliton fission. We anticipate that kindred experimental and numerical studies might be implemented in other dispersive wave guides governed by nonlinearity.
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