The Orbital Stability of Elliptic Solutions of the Focusing Nonlinear Schrödinger Equation

DOI10.1137/19M1240757zbMath1437.37096arXiv1901.08702WikidataQ126413362 ScholiaQ126413362MaRDI QIDQ5207544

Jeremy Upsal, Bernard Deconinck

Publication date: 3 January 2020

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.08702

zbMATH Keywords

integrabilityLyapunov functionalNLS equationorbital stabilityspectral stabilityelliptic solutionssubharmonic perturbations

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55)

Related Items (16)

Orbital stability and instability of periodic wave solutions for ϕ4n -models ⋮ Orbital stability and instability of periodic wave solutions for the \(\phi^4\)-model ⋮ Hamiltonian Spectral Flows, the Maslov Index, and the Stability of Standing Waves in the Nonlinear Schrodinger Equation ⋮ Multi-elliptic-dark soliton solutions of the defocusing nonlinear Schrödinger equation ⋮ The multi elliptic‐localized solutions and their asymptotic behaviors for the mKdV equation ⋮ Spectral stability of elliptic solutions to the short-pulse equation ⋮ Exact periodic wave solutions of the cubic-quintic Zakharov equation and their evolution with Hamilton energy ⋮ Stability of periodic waves for the defocusing fractional cubic nonlinear Schrödinger equation ⋮ Stability of elliptic function solutions for the focusing modified KdV equation ⋮ Modulational instability of periodic standing waves in the derivative NLS equation ⋮ Stability of elliptic solutions to the sinh-Gordon equation ⋮ Benjamin-Feir instability of Stokes waves ⋮ Full description of Benjamin-Feir instability of Stokes waves in deep water ⋮ The orbital stability of the periodic traveling wave solutions to the defocusing complex modified Korteweg-de Vries equation ⋮ Stability of elliptic solutions to the defocusing fourth order nonlinear Schrödinger equation ⋮ Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrödinger equation

Uses Software

• DLMF

Cites Work

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