Slow modulations of periodic waves in Hamiltonian PDEs, with application to capillary fluids

DOI10.1007/s00332-014-9203-zzbMath1308.35021arXiv1303.6467OpenAlexW2144909291MaRDI QIDQ457111

Pascal Noble, Sylvie Benzoni-Gavage, Luis Miguel Rodrigues

Publication date: 26 September 2014

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.6467

zbMATH Keywords

Eulerian coordinatesLagrangian coordinatesspectral stabilitymodulational instabilityEuler-Korteweg systemWhitham modulated equations

Mathematics Subject Classification ID

Related Items (22)

Behavior of periodic solutions of viscous conservation laws under localized and nonlocalized perturbations ⋮ Rigorous justification of the Whitham modulation equations for equations of Whitham type ⋮ Hyperbolicity study of the modulation equations for the Benjamin–Bona–Mahony equation ⋮ Spectral validation of the Whitham equations for periodic waves of lattice dynamical systems ⋮ Stability of periodic waves in Hamiltonian PDEs of either long wavelength or small amplitude ⋮ Dispersive and Diffusive-Dispersive Shock Waves for Nonconvex Conservation Laws ⋮ Spectral instability of small-amplitude periodic waves of the electronic Euler–Poisson system ⋮ Discontinuous shock solutions of the Whitham modulation equations as zero dispersion limits of traveling waves ⋮ Linear asymptotic stability and modulation behavior near periodic waves of the Korteweg-de Vries equation ⋮ Slow modulations of periodic waves in Hamiltonian PDEs, with application to capillary fluids ⋮ Validity of the hyperbolic Whitham modulation equations in Sobolev spaces ⋮ Hyperbolicity of the modulation equations for the Serre-Green-Naghdi model ⋮ Modulated equations of Hamiltonian PDEs and dispersive shocks ⋮ Spectral stability of inviscid roll waves ⋮ A proof of validity for multiphase Whitham modulation theory ⋮ Stability of viscous St. Venant roll waves: from onset to infinite Froude number limit ⋮ Stability of traveling wave solutions of nonlinear dispersive equations of NLS type ⋮ Global existence of finite energy weak solutions to the quantum Navier-Stokes equations with non-trivial far-field behavior ⋮ Modulational Instability of Viscous Fluid Conduit Periodic Waves ⋮ A rapid numerical method for solving Serre–Green–Naghdi equations describing long free surface gravity waves ⋮ Genuine nonlinearity and its connection to the modified Korteweg–de Vries equation in phase dynamics ⋮ About plane periodic waves of the nonlinear Schrödinger equations

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