Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves

DOI10.1088/0951-7715/29/9/2798zbMath1391.35354arXiv1505.01785OpenAlexW3106084668MaRDI QIDQ2821963

Alexander Tovbis, E. G. Khamis, Gennady A. El

Publication date: 26 September 2016

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.01785

zbMATH Keywords

Riemann-Hilbert problemsemi-classical limitmodulational instabilitysteepest-descent methodPeregrine solitondispersive shock wavesWitham equations

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Riemann-Hilbert problems in context of PDEs (35Q15) Soliton solutions (35C08)

Related Items (11)

Effective integration of ultra-elliptic solutions of the focusing nonlinear Schrödinger equation ⋮ Peregrine solitons and gradient catastrophes in discrete nonlinear Schrödinger systems ⋮ On the spectrum of the periodic focusing Zakharov-Shabat operator ⋮ Elliptic finite-band potentials of a non-self-adjoint Dirac operator ⋮ Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations ⋮ On minimal energy solutions to certain classes of integral equations related to soliton gases for integrable systems* ⋮ Rogue waves generation through multiphase solutions degeneration for the derivative nonlinear Schrödinger equation ⋮ Numerical analysis of the Hirota equation: Modulational instability, breathers, rogue waves, and interactions ⋮ The finite-gap method and the periodic NLS Cauchy problem of anomalous waves for a finite number of unstable modes ⋮ Soliton gas in integrable dispersive hydrodynamics ⋮ Modulation theory and resonant regimes for dispersive shock waves in nematic liquid crystals

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