Nonlinear modulational stability of periodic traveling-wave solutions of the generalized Kuramoto-Sivashinsky equation
From MaRDI portal
Publication:2442589
DOI10.1016/j.physd.2013.04.011zbMath1304.35184arXiv1203.3795OpenAlexW2010115551MaRDI QIDQ2442589
Kevin Zumbrun, Blake Barker, Mathew A. Johnson, Pascal Noble, Luis Miguel Rodrigues
Publication date: 4 April 2014
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1203.3795
Kuramoto-Sivashinsky equationnonlinear stabilitySwift-Hohenberg equationperiodic traveling wavesWhitham modulation equationsnumerical Evans functionnumerical time evolution studiesspectral and nonlinear stabilities
Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) Traveling wave solutions (35C07)
Related Items
Dynamic transitions of generalized Kuramoto-Sivashinsky equation, Nonlinear dynamics of a dispersive anisotropic Kuramoto–Sivashinsky equation in two space dimensions, Evans function computation for the stability of travelling waves, Periodic multi-pulses and spectral stability in Hamiltonian PDEs with symmetry, Linear modulational and subharmonic dynamics of spectrally stable Lugiato-Lefever periodic waves, Modulating traveling fronts for the Swift-Hohenberg equation in the case of an additional conservation law, Second-kind equilibrium states of the Kuramoto-Sivashinsky equation with homogeneous Neumann boundary conditions, Robust Stackelberg controllability for the Kuramoto-Sivashinsky equation, Behavior of periodic solutions of viscous conservation laws under localized and nonlocalized perturbations, Numerical proof of stability of roll waves in the small-amplitude limit for inclined thin film flow, Nonlinear modulational dynamics of spectrally stable Lugiato-Lefever periodic waves, Subharmonic dynamics of wave trains in the Korteweg‐de Vries/Kuramoto‐Sivashinsky equation, Exponential Asymptotic Stability of Riemann Shocks of Hyperbolic Systems of Balance Laws, Unstable Stokes waves, Stability of periodic Kuramoto-Sivashinsky waves, Local attractors of one of the original versions of the Kuramoto-Sivashinsky equation, Nonlocalized modulation of periodic reaction diffusion waves: nonlinear stability, Pointwise asymptotic behavior of modulated periodic reaction-diffusion waves, Pointwise stability estimates for periodic traveling wave solutions of systems of viscous conservation laws, Modulation Equations Near the Eckhaus Boundary: The KdV Equation, Existence and stability of periodic planar standing waves in phase-transitional elasticity with strain-gradient effects .I : General theory, \(O(2)\)-Hopf bifurcation for a model of cellular shock instability, On the dynamics of traveling fronts arising in nanoscale pattern formation, Existence and stability of periodic planar standing waves in phase-transitional elasticity with strain-gradient effects. II: Examples, Spectral stability of inviscid roll waves, Stability of viscous St. Venant roll waves: from onset to infinite Froude number limit, Nonnegative weak solutions of thin-film equations related to viscous flows in cylindrical geometries, \(L^1(\mathbb{R})\)-nonlinear stability of nonlocalized modulated periodic reaction-diffusion waves, Nonlinear dynamics of surfactant-laden two-fluid Couette flows in the presence of inertia, 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, Convex entropy, Hopf bifurcation, and viscous and inviscid shock stability, Viscous Hyperstabilization of Detonation Waves in One Space Dimension, Coherent Structures in Nonlocal Dispersive Active-Dissipative Systems, About plane periodic waves of the nonlinear Schrödinger equations
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Behavior of periodic solutions of viscous conservation laws under localized and nonlocalized perturbations
- Stability of periodic Kuramoto-Sivashinsky waves
- On the modulation equations and stability of periodic generalized Korteweg-de Vries waves via Bloch decompositions
- Spectral analysis for periodic solutions of the Cahn-Hilliard equation on \(\mathbb R\)
- Diffusive mixing of periodic wave trains in reaction-diffusion systems
- 2-modified characteristic Fredholm determinants, Hill's method, and the periodic Evans function of Gardner
- Nonlinear stability of spatially-periodic traveling-wave solutions of systems of reaction-diffusion equations
- Metastability of solitary roll wave solutions of the St. Venant equations with viscosity
- Chemical oscillations, waves, and turbulence
- SpectrUW: a laboratory for the numerical exploration of spectra of linear operators
- Self-similar decay of spatially localized perturbations of the Nusselt solution for the inclined film problem
- Stability and asymptotic behavior of periodic traveling wave solutions of viscous conservation laws in several dimensions
- Nonlinear stability of periodic traveling wave solutions of systems of viscous conservation laws in the generic case
- KdV cnoidal waves are spectrally stable
- Semigroups of linear operators and applications to partial differential equations
- Geometric theory of semilinear parabolic equations
- Attractors and transients for a perturbed periodic KdV equation: A nonlinear spectral analysis
- Model equation of surface waves of viscous fluid down an inclined plane
- Instability and stability of rolls in the Swift-Hohenberg equation
- Stability of periodic solutions of conservation laws with viscosity: analysis of the Evans function
- Stability of periodic solutions of conservation laws with viscosity: Pointwise bounds on the Green function
- Linear stability of steady states for thin film and Cahn-Hilliard type equations
- Self-similar decay of localized perturbations in the integral boundary layer equation
- Laminarizing effects of dispersion in an active-dissipative nonlinear medium
- On the structure of the spectra of periodic travelling waves
- Stability of periodic waves governed by the modified Kawahara equation
- Diffusive stability of spatial periodic solutions of the Swift-Hohenberg equation
- Nonlocalized modulation of periodic reaction diffusion waves: nonlinear stability
- Nonlocalized modulation of periodic reaction diffusion waves: the Whitham equation
- A sharp stability criterion for soliton-type propagating phase boundaries in Korteweg's model
- An efficient shooting algorithm for Evans function calculations in large systems
- Numerical testing of the stability of viscous shock waves
- Convergence of Hill's Method for Nonselfadjoint Operators
- Nonlinear Stability of Periodic Traveling-Wave Solutions of Viscous Conservation Laws in Dimensions One and Two
- Nonlinear Stability of Viscous Roll Waves
- Evolution of Small Periodic Disturbances into Roll Waves in Channel Flow with Internal Dissipation*
- Rigorous Justification of the Whitham Modulation Equations for the Generalized Korteweg-de Vries Equation
- 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
- Travelling-waves of the Kuramoto-Sivashinsky, equation: period-multiplying bifurcations
- Renormalization group and asymptotics of solutions of nonlinear parabolic equations
- Spectral analysis of long wavelength periodic waves and applications.
- Spectral Stability of Periodic Solutions of Viscous Conservation Laws: Large Wavelength Analysis
- Eigenvalues, and instabilities of solitary waves
- Attractors for modulation equations on unbounded domains-existence and comparison
- Whitham's modulation equations and stability of periodic wave solutions of the Korteweg-de Vries-Kuramoto-Sivashinsky Equation
- Spectral stability of periodic wave trains of the Korteweg-de Vries/Kuramoto-Sivashinsky equation in the Korteweg-de Vries limit
- Long-time persistence of Korteweg–de Vries solitons as transient dynamics in a model of inclined film flow
- On the stability of periodic travelling waves with large spatial period
- Undercompressive shocks in thin film flows.
- The motion of weakly interacting pulses in reaction-diffusion systems