聚焦介质中孤子与色散激波的非线性相互作用
Nonlinear interactions between solitons and dispersive shocks in focusing media
摘要：
利用一维非线性薛定谔方程研究了聚焦介质中由初始不连续性产生的色散激波与孤子的非线性相互作用。结果表明，当孤子从非零背景区域向零背景区域传播时，它们总是通过激波结构而不产生色散辐射。然而，它们的性质（如振幅、速度和形状）在此过程中会发生变化。当孤立子从零背景区域向非零背景区域传播时，也会产生类似的效应，不同之处在于，取决于它的初速度，在这种情况下，孤立子可能会无限期地被困在类似激波的结构中。在所有情况下，新的孤子特性可以确定解析。通过与数值模拟结果的比较，验证了结果的正确性。
英文摘要：
Nonlinear interactions in focusing media between traveling solitons and the dispersive shocks produced by an initial discontinuity are studied using the one-dimensional nonlinear Schrodinger equation. It is shown that, when solitons travel from a region with nonzero background towards a region with zero background, they always pass through the shock structure without generating dispersive radiation. However, their properties (such as amplitude, velocity and shape) change in the process. A similar effect arises when solitons travel from a region with zero background towards a region with nonzero background, except that, depending on its initial velocity, in this case the soliton may remain trapped inside the shock-like structure indefinitely. In all cases, the new soliton properties can be determined analytically. The results are validated by comparison with numerical simulations.
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