Excitation of Peregrine-type waveforms from vanishing initial conditions in the presence of periodic forcing

Abstract

We show by direct numerical simulations that spatiotemporally localized wave forms, strongly reminiscent of the Peregrine rogue wave, can be excited by vanishing initial conditions for the periodically driven nonlinear Schrödinger equation. The emergence of the Peregrine-type waveforms can be potentially justified, in terms of the existence and modulational instability of spatially homogeneous solutions of the model, and the continuous dependence of the localized initial data for small time intervals. We also comment on the persistence of the above dynamics, under the presence of small damping effects, and justify, that this behavior should be considered as far from approximations of the corresponding integrable limit.

References in corpus (14)

• Observation of an Inverse Energy Cascade in Developed Acoustic Turbulence in Superfluid Helium
• Universal nature of the nonlinear stage of modulational instability
• Universal Peregrine soliton structure in nonlinear pulse compression in optical fiber
• Approximate rogue wave solutions of the forced and damped Nonlinear Schrödinger equation for water waves
• Rogue waves, rational solitons, and modulational instability in an integrable fifth-order nonlinear Schroedinger equation
• Instabilities, solitons, and rogue waves in PT-coupled nonlinear waveguides
• Nonlinear fast growth of water waves under wind forcing
• Nonlinear spectral analysis of Peregrine solitons observed in optics and in hydrodynamic experiments
• Wave amplification in the framework of forced nonlinear Schrodinger equation: the rogue wave context
• Floquet Analysis of Kuznetsov--Ma breathers: A Path Towards Spectral Stability of Rogue Waves
• Breather-like solitons extracted from the Peregrine rogue wave
• Nonconservative higher-order hydrodynamic modulation instability
• High-power pulse trains excited by modulated continuous waves
• Stabilization of the Peregrine soliton and Kuznetsov-Ma breathers by means of nonlinearity and dispersion management

Cited by in corpus (3)

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