Direct Characterization of Spectral Stability of Small-Amplitude Periodic Waves in Scalar Hamiltonian Problems via Dispersion Relation

DOI10.1137/18M1188161zbMath1426.37053arXiv1906.04453MaRDI QIDQ5231337

Olga Trichtchenko, Richard Kollár, Bernard Deconinck

Publication date: 26 August 2019

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

Full work available at URL: https://arxiv.org/abs/1906.04453

zbMATH Keywords

dispersion relationinfinite-dimensional Hamiltonian systemspectral stabilityperiodic waves

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) General topics in linear spectral theory for PDEs (35P05) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45)

Related Items (8)

Instability of small-amplitude periodic waves from fold-Hopf bifurcation ⋮ Spectral instability of small-amplitude periodic waves for hyperbolic non-Fickian diffusion advection models with logistic source ⋮ Perturbation of the spectra for asymptotically constant differential operators and applications ⋮ A Reformulated Krein Matrix for Star-Even Polynomial Operators with Applications ⋮ A Method for Identifying Stability Regimes Using Roots of a Reduced-Order Polynomial ⋮ High-Frequency Instabilities of the Kawahara Equation: A Perturbative Approach ⋮ A new Evans function for quasi-periodic solutions of the linearised sine-Gordon equation ⋮ Existence and spectral instability of bounded spatially periodic traveling waves for scalar viscous balance laws

Uses Software

• DLMF

Cites Work

• Unnamed Item
• High-frequency instabilities of small-amplitude solutions of Hamiltonian PDEs
• Computing spectra of linear operators using the Floquet-Fourier-Hill method
• Spectral stability of wave trains in the Kawahara equation
• Stability theory of solitary waves in the presence of symmetry. II
• On the spectra of periodic waves for infinite-dimensional Hamiltonian systems
• KdV cnoidal waves are spectrally stable
• The Hamiltonian Hopf bifurcation
• Stability theory of solitary waves in the presence of symmetry. I
• Spectral and dynamical stability of nonlinear waves
• On the Spectral and Orbital Stability of Spatially Periodic Stationary Solutions of Generalized Korteweg-de Vries Equations
• The instability of periodic surface gravity waves
• The Stability Analysis of the Periodic Traveling Wave Solutions of the mKdV Equation
• Generic bifurcation of Hamiltonian vector fields with symmetry
• Nonlinear Waves, Solitons and Chaos
• Stability of Periodic Traveling Wave Solutions to the Kawahara Equation
• Nonlinear Stability of Periodic Traveling Wave Solutions of the Generalized Korteweg–de Vries Equation
• Spectral Stability of Nonlinear Waves in KdV‐Type Evolution Equations
• Graphical Krein Signature Theory and Evans--Krein Functions
• A Hamiltonian–Krein (Instability) Index Theory for Solitary Waves to KdV‐Like Eigenvalue Problems
• Inertia law for spectral stability of solitary waves in coupled nonlinear Schrödinger equations
• Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems
• Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems

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