Spectral transverse instability of solitary waves in Korteweg fluids

DOI10.1016/j.jmaa.2009.07.023zbMath1180.35451OpenAlexW2025230142MaRDI QIDQ1034047

Sylvie Benzoni-Gavage

Publication date: 10 November 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.07.023

zbMATH Keywords

Evans functionHamiltonian structuresolitonorbital stabilitylinearized stabilitycapillarity

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Capillarity (surface tension) for incompressible viscous fluids (76D45) Hydrodynamic stability (76E99) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Soliton solutions (35C08)

Related Items (11)

Weak Solutions to Problems Involving Inviscid Fluids ⋮ Well/Ill Posedness for the Euler-Korteweg-Poisson System and Related Problems ⋮ Stability of traveling waves of nonlinear Schrödinger equation with nonzero condition at infinity ⋮ Transverse nonlinear instability of Euler-Korteweg solitons ⋮ The Boussinesq systems on the background of a line solitary wave ⋮ Stability of periodic waves in Hamiltonian PDEs of either long wavelength or small amplitude ⋮ Phase transitions and traveling waves in compressible fluids ⋮ Standing solitary Euler-Korteweg waves are unstable ⋮ High Mach number limit for Korteweg fluids with density dependent viscosity ⋮ Relative energy for the Korteweg theory and related Hamiltonian flows in gas dynamics ⋮ About plane periodic waves of the nonlinear Schrödinger equations

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