The stability spectrum for elliptic solutions to the sine-Gordon equation

DOI10.1016/j.physd.2017.08.010zbMath1378.35028arXiv1705.04586OpenAlexW2613931935MaRDI QIDQ1691283

Peter McGill, Benjamin L. Segal, Bernard Deconinck

Publication date: 15 January 2018

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

Full work available at URL: https://arxiv.org/abs/1705.04586

zbMATH Keywords

stabilitysine-Gordon equationelliptic solutions

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Second-order nonlinear hyperbolic equations (35L70)

Related Items (13)

Orbital stability and instability of periodic wave solutions for ϕ4n -models ⋮ Orbital stability and instability of periodic wave solutions for the \(\phi^4\)-model ⋮ Multi-elliptic-dark soliton solutions of the defocusing nonlinear Schrödinger equation ⋮ Spectral stability of elliptic solutions to the short-pulse equation ⋮ Legendre spectral element method for solving sine-Gordon equation ⋮ Nondegeneracy and stability of antiperiodic bound states for fractional nonlinear Schrödinger equations ⋮ Localized structures on librational and rotational travelling waves in the sine-Gordon equation ⋮ The stability spectrum for elliptic solutions to the focusing NLS equation ⋮ The Orbital Stability of Elliptic Solutions of the Focusing Nonlinear Schrödinger Equation ⋮ Stability of elliptic solutions to the sinh-Gordon equation ⋮ 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 ⋮ On the elliptic-localized solutions of the sine-Gordon equation

Uses Software

• DLMF

Cites Work

• On the stability analysis of periodic sine-Gordon traveling waves
• The orbital stability of the cnoidal waves of the Korteweg-de Vries equation
• Spectral and modulational stability of periodic wavetrains for the nonlinear Klein-Gordon equation
• KdV cnoidal waves are spectrally stable
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Elliptic functions and applications
• Spectral and dynamical stability of nonlinear waves
• The stability spectrum for elliptic solutions to the focusing NLS equation
• The Stability Analysis of the Periodic Traveling Wave Solutions of the mKdV Equation
• Method for Solving the Sine-Gordon Equation in Laboratory Coordinates
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Stability of Periodic Waves of 1D Cubic Nonlinear Schrödinger Equations
• Introduction to Applied Nonlinear Dynamical Systems and Chaos
• Elliptic solutions of the defocusing NLS equation are stable
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