Periodic standing waves in the focusing nonlinear Schrödinger equation: rogue waves and modulation instability

DOI10.1016/j.physd.2020.132378zbMath1490.35399OpenAlexW3005345505MaRDI QIDQ2077562

Robert E. White, Jinbing Chen, Dmitry E. Pelinovsky

Publication date: 21 February 2022

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2020.132378

zbMATH Keywords

rogue wavesmodulation instabilityperiodic standing waves

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Initial-boundary value problems for higher-order parabolic equations (35K35) NLS equations (nonlinear Schrödinger equations) (35Q55) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Finite difference methods for boundary value problems involving PDEs (65N06) Elliptic functions and integrals (33E05) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41)

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Uses Software

• DLMF
• rogue-waves

Cites Work

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• Modulation instability: The beginning
• The stability spectrum for elliptic solutions to the focusing NLS equation
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• Nonlinearizations of spectral problems of the nonlinear Schrödinger equation and the real-valued modified Korteweg–de Vries equation
• Finite‐Dimensional Integrable Hamiltonian Systems Related to the Nonlinear Schrödinger Equation
• Universal Behavior of Modulationally Unstable Media
• Rogue periodic waves of the focusing nonlinear Schrödinger equation
• Rogue periodic waves of the modified KdV equation
• Multi‐breather and high‐order rogue waves for the nonlinear Schrödinger equation on the elliptic function background
• The finite-gap method and the periodic NLS Cauchy problem of anomalous waves for a finite number of unstable modes
• A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation
• General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation
• Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation
• Multi-rogue waves solutions: from the NLS to the KP-I equation
• On improving the effectiveness of periodic solutions of the NLS and DNLS equations

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