Dark Solitons, Dispersive Shock Waves, and Transverse Instabilities
Dark Solitons, Dispersive Shock Waves, and Transverse Instabilities
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暗孤子、色散冲击波和横向不稳定性
DOI：
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发表时间：
2011
影响因子：
1.6
通讯作者：
B. Ilan
中科院分区：
文献类型：
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作者：
M. Hoefer;B. Ilan
考虑了 (2+1) 维散焦非线性 Schrodinger/Gross–Pitaevskii˘ (NLS/GP) 方程的暗孤子横向不稳定性的性质。特别注意小（浅）振幅范围，它限制了 Kadomtsev-Petviashvili (KP) 方程。我们对线性 NLS/GP 方程的特征值进行了分析和数值研究。浅孤子的色散关系是在 KP 极限之外渐近获得的。这产生（1）不稳定扰动的最大增长率和相关波数以及（2）对流和绝对不稳定性之间的分界线。暗孤子的不稳定性与斜色散激波（DSW）解的不稳定性直接相关。通过直接模拟 NLS/GP 方程，对静态和非静态倾斜 DSW 进行分析构造和数值研究。研究发现，静止和非静止斜向DSWs在浅层和高海拔地区具有相同的跳跃条件。
The nature of transverse instabilities of dark solitons for the (2+1)-dimensional defocusing nonlinear Schrodinger/Gross–Pitaevskii˘ (NLS/GP) equation is considered. Special attention is given to the small (shallow) amplitude regime, which limits to the Kadomtsev–Petviashvili (KP) equation. We study analytically and numerically the eigenvalues of the linearized NLS/GP equation. The dispersion relation for shallow solitons is obtained asymptotically beyond the KP limit. This yields (1) the maximal growth rate and associated wavenumber of unstable perturbations and (2) the separatrix between convective and absolute instabilities. The instability properties of the dark soliton are directly related to those of oblique dispersive shock wave (DSW) solutions. Stationary and nonstationary oblique DSWs are constructed analytically and investigated numerically by direct simulations of the NLS/GP equation. It is found that stationary and nonstationary oblique DSWs have the same jump conditions in the shallow and hyp...