Spectral instability of the peaked periodic wave in the reduced Ostrovsky equations

DOI10.1090/proc/14937zbMath1454.35024arXiv1903.09660OpenAlexW3094031762MaRDI QIDQ5130856

Anna Geyer, Dmitry E. Pelinovsky

Publication date: 29 October 2020

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.09660

zbMATH Keywords

orbital stabilityspectral stabilityspectral instabilityreduced Ostrovsky equationpeaked periodic wavetruncated spectral problem

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Stability in context of PDEs (35B35) Periodic solutions to PDEs (35B10)

Related Items (8)

The stability of the b-family of peakon equations ⋮ Stability of periodic peaked solitary waves for a cubic Camassa-Holm-type equation ⋮ Spectral Instability of Peakons in the $b$-Family of the Camassa--Holm Equations ⋮ Existence, regularity and symmetry of periodic traveling waves for Gardner-Ostrovsky type equations ⋮ Superharmonic instability of stokes waves ⋮ Instability of \(H^1\)-stable periodic peakons for the \(\mu\)-Camassa-Holm equation ⋮ Stability of periodic peakons for a nonlinear quartic \(\mu\)-Camassa-Holm equation ⋮ Growth of Perturbations to the Peaked Periodic Waves in the Camassa--Holm Equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the spectral problem \(\mathcal{L}u=\lambda u'\) and applications
• Global existence of small-norm solutions in the reduced Ostrovsky equation
• Well-posedness and small data scattering for the generalized Ostrovsky equation
• Existence of a highest wave in a fully dispersive two-way shallow water model
• Spectral stability of periodic waves in the generalized reduced Ostrovsky equation
• Orbital stability of periodic waves in the class of reduced Ostrovsky equations
• Periodic Traveling Waves of the Regularized Short Pulse and Ostrovsky Equations: Existence and Stability
• Wave Breaking in the Ostrovsky–Hunter Equation
• Evolution Equations for Weakly Nonlinear, Long Internal Waves in a Rotating Fluid
• On the Hamiltonian–Krein index for a non-self-adjoint spectral problem
• Spectral Stability for Classical Periodic Waves of the Ostrovsky and Short Pulse Models
• Beyond the KdV: Post-explosion development
• Linear Instability and Uniqueness of the Peaked Periodic Wave in the Reduced Ostrovsky Equation
• The Reduced Ostrovsky Equation: Integrability and Breaking
• Functional Analysis

This page was built for publication: Spectral instability of the peaked periodic wave in the reduced Ostrovsky equations