Stability of periodic Kuramoto-Sivashinsky waves

DOI10.1016/j.aml.2011.10.026zbMath1238.35094arXiv1012.4775OpenAlexW4298879597MaRDI QIDQ419077

Blake Barker, Kevin Zumbrun, Mathew A. Johnson, Pascal Noble, Luis Miguel Rodrigues

Publication date: 18 May 2012

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

Full work available at URL: https://arxiv.org/abs/1012.4775

zbMATH Keywords

periodic wavesKuramoto-Sivashinsky equationsmodulational stability

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Stability in context of PDEs (35B35) Traveling wave solutions (35C07)

Related Items (13)

Second-kind equilibrium states of the Kuramoto-Sivashinsky equation with homogeneous Neumann boundary conditions ⋮ Behavior of periodic solutions of viscous conservation laws under localized and nonlocalized perturbations ⋮ Subharmonic dynamics of wave trains in the Korteweg‐de Vries/Kuramoto‐Sivashinsky equation ⋮ An Evans function for the linearised 2D Euler equations using Hill's determinant ⋮ Nonlocalized modulation of periodic reaction diffusion waves: nonlinear stability ⋮ Nonlocalized modulation of periodic reaction diffusion waves: the Whitham equation ⋮ Computing Evans functions numerically via boundary-value problems ⋮ Nonlinear modulational stability of periodic traveling-wave solutions of the generalized Kuramoto-Sivashinsky equation ⋮ \(O(2)\)-Hopf bifurcation for a model of cellular shock instability ⋮ Existence and stability of periodic planar standing waves in phase-transitional elasticity with strain-gradient effects. II: Examples ⋮ Stability of viscous St. Venant roll waves: from onset to infinite Froude number limit ⋮ Spectral stability of periodic wave trains of the Korteweg-de Vries/Kuramoto-Sivashinsky equation in the Korteweg-de Vries limit ⋮ Convergence as period goes to infinity of spectra of periodic traveling waves toward essential spectra of a homoclinic limit

Uses Software

• SpectrUW

Cites Work

• SpectrUW: a laboratory for the numerical exploration of spectra of linear operators
• Nonlinear stability of periodic traveling wave solutions of systems of viscous conservation laws in the generic case
• On the structure of the spectra of periodic travelling waves
• A sharp stability criterion for soliton-type propagating phase boundaries in Korteweg's model
• Nonlinear modulational stability of periodic traveling-wave solutions of the generalized Kuramoto-Sivashinsky equation
• Stability of compressive and undercompressive thin film travelling waves
• Nonlinear Stability of Viscous Roll Waves
• The dynamics of modulated wave trains
• Viscoelastic behaviour of cellular solutions to the Kuramoto-Sivashinsky model
• Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations
• Spectral Stability of Periodic Solutions of Viscous Conservation Laws: Large Wavelength Analysis
• Long-time persistence of Korteweg–de Vries solitons as transient dynamics in a model of inclined film flow

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