Stability of Periodic Traveling Waves for Nonlinear Dispersive Equations

DOI10.1137/12090215XzbMath1327.35032arXiv1303.4765OpenAlexW2137311213MaRDI QIDQ2947452

Mathew A. Johnson, Vera Mikyoung Hur

Publication date: 24 September 2015

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

Full work available at URL: https://arxiv.org/abs/1303.4765

zbMATH Keywords

fractional dispersionperiod preserving perturbations

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Periodic solutions to PDEs (35B10) Traveling wave solutions (35C07)

Related Items (23)

Modulational instability in nonlinear nonlocal equations of regularized long wave type ⋮ Periodic waves in the fractional modified Korteweg-de Vries equation ⋮ A Note on the Local Well-Posedness for the Whitham Equation ⋮ Sufficient conditions for orbital stability of periodic traveling waves ⋮ Periodic Waves of the Modified KdV Equation as Minimizers of a New Variational Problem ⋮ Periodic multi-pulses and spectral stability in Hamiltonian PDEs with symmetry ⋮ Numerical generation of periodic traveling wave solutions of some nonlinear dispersive wave systems ⋮ Stability of smooth periodic travelling waves in the Camassa–Holm equation ⋮ On the existence, uniqueness, and stability of periodic waves for the fractional Benjamin–Bona–Mahony equation ⋮ Stability of periodic waves for the defocusing fractional cubic nonlinear Schrödinger equation ⋮ Global well-posedness for \(H^{-1}(\mathbb{R})\) perturbations of KdV with exotic spatial asymptotics ⋮ Nonlinear modulational instability of dispersive PDE models ⋮ Nondegeneracy and stability of antiperiodic bound states for fractional nonlinear Schrödinger equations ⋮ Numerical bifurcation and stability for the capillary-gravity Whitham equation ⋮ Modulational Instability and Variational Structure ⋮ Orbital stability of periodic traveling-wave solutions for a dispersive equation ⋮ Green's function for the fractional KdV equation on the periodic domain via Mittag-Leffler function ⋮ Convergence of Petviashvili's Method near Periodic Waves in the Fractional Korteweg--de Vries Equation ⋮ Stability of periodic waves for the fractional KdV and NLS equations ⋮ On the Cauchy problem for the fractional Camassa-Holm equation ⋮ ON THE INSTABILITY OF PERIODIC WAVES FOR DISPERSIVE EQUATIONS—REVISITED ⋮ Instability, index theorem, and exponential trichotomy for Linear Hamiltonian PDEs ⋮ Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrödinger equation

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