Transverse Instability of Rogue Waves

Abstract

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 Schrodinger 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.

arXiv commentSupplementary Material available on Publisher's website

References in corpus (5)

• Observation of an Inverse Energy Cascade in Developed Acoustic Turbulence in Superfluid Helium
• Vector Rogue Waves and Baseband Modulation Instability in the Defocusing Regime
• Spontaneously generated X-shaped light bullets
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Cited by in corpus (5)

• Dissipative structures in topological lattices of nonlinear optical resonators
• Theoretical and numerical evidence for the potential realization of the Peregrine soliton in repulsive two-component Bose-Einstein condensates
• Statistics of rogue waves in isotropic wave fields
• Evidence of 1+1D photorefractive stripe solitons deep in the Kerr limit
• Rogue waves collision under incident momentum modulation in two-component Bose-Einstein condensates