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非线性薛定谔系统中存在非零背景时的波不稳定性。

Wave instabilities in the presence of non vanishing background in nonlinear Schrödinger systems.

作者信息

Trillo S, Gongora J S Totero, Fratalocchi A

机构信息

Dipartimento di Ingegneria, Università di Ferrara, Via Saragat 1, 44122 Ferrara, Italy.

PRIMALIGHT, Faculty of Electrical Engineering; Applied Mathematics and Computational Science, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia.

出版信息

Sci Rep. 2014 Dec 3;4:7285. doi: 10.1038/srep07285.

Abstract

We investigate wave collapse ruled by the generalized nonlinear Schrödinger (NLS) equation in 1+1 dimensions, for localized excitations with non-zero background, establishing through virial identities a new criterion for blow-up. When collapse is arrested, a semiclassical approach allows us to show that the system can favor the formation of dispersive shock waves. The general findings are illustrated with a model of interest to both classical and quantum physics (cubic-quintic NLS equation), demonstrating a radically novel scenario of instability, where solitons identify a marginal condition between blow-up and occurrence of shock waves, triggered by arbitrarily small mass perturbations of different sign.

摘要

我们研究了一维空间中由广义非线性薛定谔(NLS)方程所支配的波塌缩现象,针对具有非零背景的局域激发,通过位力恒等式建立了一个新的爆破解判定准则。当塌缩被阻止时,一种半经典方法使我们能够证明该系统有利于色散激波的形成。通过一个对经典物理和量子物理都有意义的模型(立方 - 五次NLS方程)对一般结果进行了说明,展示了一种全新的不稳定性情形,即孤子确定了爆聚和激波出现之间的临界条件,该条件由任意小的不同符号质量微扰触发。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4b41/4252897/d9bac74b4a0c/srep07285-f1.jpg

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