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Karachalios NI, Kyriazopoulos P, Vetas K. Excitation of Peregrine-Type Waveforms from Vanishing Initial Conditions in the Presence of Periodic Forcing. ACTA ACUST UNITED AC 2019. [DOI: 10.1515/zna-2018-0540] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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.
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Affiliation(s)
- Nikos I. Karachalios
- Department of Mathematics , University of the Aegean , Karlovassi, GR 83200 Samos , Greece
| | - Paris Kyriazopoulos
- Department of Mathematics , University of the Aegean , Karlovassi, GR 83200 Samos , Greece
| | - Konstantinos Vetas
- Department of Mathematics , University of the Aegean , Karlovassi, GR 83200 Samos , Greece
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Qu Z, Hu G, Yang G, Qin G. Phase effect in taming nonautonomous chaos by weak harmonic perturbations. PHYSICAL REVIEW LETTERS 1995; 74:1736-1739. [PMID: 10057744 DOI: 10.1103/physrevlett.74.1736] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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