Ablowitz Mark J, Cole Justin T
Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA.
Department of Mathematics, University of Colorado, Colorado Springs, Colorado 80918, USA.
Phys Rev Lett. 2021 Sep 3;127(10):104101. doi: 10.1103/PhysRevLett.127.104101.
Rogue waves are abnormally large waves which appear unexpectedly and have attracted considerable attention, particularly in recent years. The one space, one time (1+1) nonlinear Schrödinger equation is often used to model rogue waves; it is an envelope description of plane waves and admits the so-called Pergerine and Kuznetov-Ma soliton solutions. However, in deep water waves and certain electromagnetic systems where there are two significant transverse dimensions, the 2+1 hyperbolic nonlinear Schrödinger equation is the appropriate wave envelope description. Here we show that these rogue wave solutions suffer from strong transverse instability at long and short frequencies. Moreover, the stability of the Peregrine soliton is found to coincide with that of the background plane wave. These results indicate that, when applicable, transverse dimensions must be taken into account when investigating rogue wave pheneomena.
rogue波是异常大的波，它们出乎意料地出现并引起了相当大的关注，尤其是近年来。一维一时间（1 + 1）非线性薛定谔方程常被用于模拟rogue波；它是平面波的包络描述，并允许所谓的佩雷格林和库兹涅托夫 - 马孤子解。然而，在有两个显著横向维度的深水波和某些电磁系统中，二维一时间（2 + 1）双曲非线性薛定谔方程才是合适的波包络描述。在这里，我们表明这些rogue波解在长频率和短频率下都遭受强烈的横向不稳定性。此外，发现佩雷格林孤子的稳定性与背景平面波的稳定性一致。这些结果表明，在适用时，研究rogue波现象时必须考虑横向维度。
