Rogue wave formation and interactions in the defocusing nonlinear Schrödinger equation with external potentials

DOI10.1016/j.aml.2020.106670zbMath1451.35201arXiv2012.09983OpenAlexW3048188629MaRDI QIDQ2006360

Zhenya Yan, Li Wang

Publication date: 8 October 2020

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.09983

zbMATH Keywords

modulational instabilityrogue wavesdefocusing nonlinear Schrödinger equation\( \mathcal{PT} \)-symmetric potentialW-shaped solitons

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton solutions (35C08)

Related Items (5)

Data-driven rogue waves and parameters discovery in nearly integrable \(\mathcal{PT}\)-symmetric Gross-Pitaevskii equations via PINNs deep learning ⋮ Interactions among the rogue waves and solitons for a \((2 + 1)\)-dimensional Maccari system in fluid mechanics and nonlinear optics ⋮ Data-driven rogue waves and parameter discovery in the defocusing nonlinear Schrödinger equation with a potential using the PINN deep learning ⋮ Multi-component nonlinear Schrödinger equations with nonzero boundary conditions: higher-order vector Peregrine solitons and asymptotic estimates ⋮ Impact of external potential and non-isospectral functions on optical solitons and modulation instability in a cubic quintic nonlinear media

Cites Work

• The Hirota equation: Darboux transform of the Riemann-Hilbert problem and higher-order rogue waves
• Water waves, nonlinear Schrödinger equations and their solutions
• The Defocusing Nonlinear Schrödinger Equation
• Rogue waves, rational solitons, and modulational instability in an integrable fifth-order nonlinear Schrödinger equation
• Numerical analysis of the Hirota equation: Modulational instability, breathers, rogue waves, and interactions
• Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex PT-invariant potential

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