Stability of periodic traveling flexural‐gravity waves in two dimensions

DOI10.1111/sapm.12233zbMath1420.35218arXiv1801.09748OpenAlexW2963172543MaRDI QIDQ4967120

Olga Trichtchenko, Jean-Marc Vanden-Broeck, Paul A. Milewski, Emilian I. Părău

Publication date: 2 July 2019

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.09748

zbMATH Keywords

nonlinear wavesnumerical methodsasymptotic analysisstability of solutionswaves under ice

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Periodic solutions to PDEs (35B10) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) NLS equations (nonlinear Schrödinger equations) (35Q55) Traveling wave solutions (35C07) Euler equations (35Q31)

Related Items (5)

Progressive flexural–gravity waves with constant vorticity ⋮ The Viscous Surface Wave Problem with Generalized Surface Energies ⋮ Effective wavelength of envelope waves on the water surface beneath an ice sheet: small amplitudes and moderate depths ⋮ Wilton ripples in weakly nonlinear dispersive models of water waves: existence and analyticity of solution branches ⋮ Nonlinear hydroelastic waves on a linear shear current at finite depth

Cites Work

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• Variational existence theory for hydroelastic solitary waves
• Stability of periodic gravity waves in the presence of surface tension
• High-frequency instabilities of small-amplitude solutions of Hamiltonian PDEs
• Computing spectra of linear operators using the Floquet-Fourier-Hill method
• Steady periodic hydroelastic waves
• Theory of two-dimensional nonlinear waves in liquid covered by ice
• Introduction to spectral theory. With applications to Schrödinger operators
• The instability of Wilton ripples
• Convergence of Hill's Method for Nonselfadjoint Operators
• The instability of periodic surface gravity waves
• Hydroelastic solitary waves in deep water
• Three Dimensional Flexural-Gravity Waves
• Comparison of five methods of computing the Dirichlet-Neumann operator for the water wave problem
• Modelling nonlinear hydroelastic waves
• Two-dimensional generalized solitary waves and periodic waves under an ice sheet
• Numerical studies of two-dimensional hydroelastic periodic and generalised solitary waves
• Gravity–Capillary Free-Surface Flows
• On the convergence of Hill’s method
• Stability of water waves
• Surface waves of large amplitude beneath an elastic sheet. Part 1. High-order series solution
• A unified transform method for solving linear and certain nonlinear PDEs
• Computations of fully nonlinear hydroelastic solitary waves on deep water
• On a new non-local formulation of water waves

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