A Method for Identifying Stability Regimes Using Roots of a Reduced-Order Polynomial

DOI10.1007/978-3-030-33536-6_12zbMath1441.35095arXiv1906.04275OpenAlexW2950069955MaRDI QIDQ3294760

Olga Trichtchenko

Publication date: 29 June 2020

Published in: Nonlinear Water Waves (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.04275

zbMATH Keywords

Hamiltonian PDEdispersionspectral stabilitySturm's theoryhigh-frequency instabilities

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Traveling wave solutions (35C07)

Cites Work

• High-frequency instabilities of small-amplitude solutions of Hamiltonian PDEs
• Computing spectra of linear operators using the Floquet-Fourier-Hill method
• The instability of Wilton ripples
• An index theorem for the stability of periodic travelling waves of Korteweg–de Vries type
• Stability of Periodic Traveling Wave Solutions to the Kawahara Equation
• Modulational Instability in the Whitham Equation for Water Waves
• Direct Characterization of Spectral Stability of Small-Amplitude Periodic Waves in Scalar Hamiltonian Problems via Dispersion Relation
• Graphical Krein Signature Theory and Evans--Krein Functions
• Introduction to Partial Differential Equations

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