Phase resonances of the NLS rogue wave recurrence in the quasisymmetric case

DOI10.1134/S0040577918090040zbMath1408.35172OpenAlexW2896106153WikidataQ129156865 ScholiaQ129156865MaRDI QIDQ1716287

Paolo Maria Santíni, Petr G. Grinevich

Publication date: 4 February 2019

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0040577918090040

zbMATH Keywords

recurrencefocusing nonlinear Schrödinger equationanomalous wavealmost symmetric configurationphase resonance

Mathematics Subject Classification ID

Shock waves and blast waves in fluid mechanics (76L05) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) NLS equations (nonlinear Schrödinger equations) (35Q55) Asymptotic expansions of solutions to PDEs (35C20) Lasers, masers, optical bistability, nonlinear optics (78A60) Resonance in context of PDEs (35B34) Soliton solutions (35C08)

Related Items (6)

The effect of loss/gain and Hamiltonian perturbations of the Ablowitz—Ladik lattice on the recurrence of periodic anomalous waves ⋮ Modulation instability, periodic anomalous wave recurrence, and blow up in the Ablowitz–Ladik lattices ⋮ The periodic N breather anomalous wave solution of the Davey–Stewartson equations; first appearance, recurrence, and blow up properties ⋮ The periodic Cauchy problem for PT-symmetric NLS, I: the first appearance of rogue waves, regular behavior or blow up at finite times ⋮ The finite-gap method and the periodic NLS Cauchy problem of anomalous waves for a finite number of unstable modes ⋮ The linear and nonlinear instability of the Akhmediev breather

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