Trillo S, Gongora J S Totero, Fratalocchi A
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.
Sci Rep. 2014 Dec 3;4:7285. doi: 10.1038/srep07285.
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.
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。
