Stability of Periodic Traveling Wave Solutions to the Kawahara Equation

DOI10.1137/18M1196121zbMath1404.76054arXiv1806.08445WikidataQ128827405 ScholiaQ128827405MaRDI QIDQ4562426

Richard Kollár, Olga Trichtchenko, Bernard Deconinck

Publication date: 20 December 2018

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.08445

zbMATH Keywords

stabilitydispersiontraveling wavesresonanceKorteweg-de VriesKawahara

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45)

Related Items

Instability of small-amplitude periodic waves from fold-Hopf bifurcation ⋮ An Evans function for the linearised 2D Euler equations using Hill's determinant ⋮ Traveling wave solutions of the Kawahara equation joining distinct periodic waves ⋮ Spectral instability of small-amplitude periodic waves of the electronic Euler–Poisson system ⋮ 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 ⋮ Well-posedness of the classical solutions for a Kawahara-Korteweg-de Vries-type equation ⋮ A new Evans function for quasi-periodic solutions of the linearised sine-Gordon equation ⋮ Well-posedness issues on the periodic modified Kawahara equation ⋮ Direct Characterization of Spectral Stability of Small-Amplitude Periodic Waves in Scalar Hamiltonian Problems via Dispersion Relation ⋮ Wilton ripples in weakly nonlinear models of water waves: existence and computation ⋮ On the solutions for a Benney-Lin type equation ⋮ ORBITAL STABILITY OF PERIODIC TRAVELING WAVE SOLUTIONS TO THE GENERALIZED LONG-SHORT WAVE EQUATIONS ⋮ Global H4 solution for the fifth-order Kudryashov–Sinelshchikov–Olver equation

Cites Work

• Unnamed Item
• High-frequency instabilities of small-amplitude solutions of Hamiltonian PDEs
• On the modulation equations and stability of periodic generalized Korteweg-de Vries waves via Bloch decompositions
• Stability and instability of solitary waves of the fifth-order KdV equation: a numerical framework
• Computing spectra of linear operators using the Floquet-Fourier-Hill method
• Spectral stability of wave trains in the Kawahara equation
• On the spectra of periodic waves for infinite-dimensional Hamiltonian systems
• Modeling nonlinear resonance: A modification to the Stokes' perturbation expansion
• The rigorous approximation of long-wavelength capillary-gravity waves
• Perturbation theory for linear operators.
• Wilton ripples in weakly nonlinear model equations
• The instability of Wilton ripples
• Modulational instabilities of periodic traveling waves in deep water
• Spectral stability of traveling water waves: analytic dependence of the spectrum
• On the Spectral and Orbital Stability of Spatially Periodic Stationary Solutions of Generalized Korteweg-de Vries Equations
• Spectral data for travelling water waves: singularities and stability
• Stability of water waves
• Weakly nonlinear non-symmetric gravity waves on water of finite depth
• Instabilities of finite-amplitude water waves
• Numerical Bifurcation and Spectral Stability of Wavetrains in Bidirectional Whitham Models
• Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
• Spectral Stability of Deep Two‐Dimensional Gravity‐Capillary Water Waves

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