Affiliation:
1. Department of Mathematics , University of the Aegean , Karlovassi, GR 83200 Samos , Greece
Abstract
Abstract
We show by direct numerical simulations that spatiotemporally localised waveforms, 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 localised 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 behaviour should be considered as far from approximations of the corresponding integrable limit.
Subject
Physical and Theoretical Chemistry,General Physics and Astronomy,Mathematical Physics
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