On the stability of periodic travelling waves with large spatial period

DOI10.1006/jdeq.2000.3855zbMath0994.34035OpenAlexW2092999826WikidataQ60143921 ScholiaQ60143921MaRDI QIDQ5935538

Björn Sandstede, Arnd Scheel

Publication date: 26 June 2001

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/6d971525742b0899fb430853d49405cfab9c05bc

zbMATH Keywords

stabilityexponential dichotomieshomoclinic bifurcation pointslarge spatial periodperiodic travelling wavesperiodic wave trains

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Reaction-diffusion equations (35K57) General spectral theory of ordinary differential operators (34L05) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Dichotomy, trichotomy of solutions to ordinary differential equations (34D09)

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Cites Work

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• Fast and slow waves in the FitzHugh-Nagumo equation
• Homoclinic bifurcation at resonant eigenvalues
• Stability of fast travelling pulse solutions of the FitzHugh-Nagumo equations
• Geometric theory of semilinear parabolic equations
• Homoclinic period blow-up in reversible and conservative systems
• Stability of pulses on optical fibers with phase-sensitive amplifiers
• Exponential dichotomies for solitary-wave solutions of semilinear elliptic equations on infinite cylinders
• Instability and stability of rolls in the Swift-Hohenberg equation
• Geometric stability analysis for periodic solutions of the Swift-Hohenberg equation
• Absolute and convective instabilities of waves on unbounded and large bounded domains
• Stability of bright solitary-wave solutions to perturbed nonlinear Schrödinger equations
• Slow-motion manifolds, dormant instability, and singular perturbations
• On the structure of the spectra of periodic travelling waves
• Diffusive stability of spatial periodic solutions of the Swift-Hohenberg equation
• Existence and stability of \(N\)-pulses on optical fibers with phase-sensitive amplifiers
• Bifurcations to \(N\)-homoclinic orbits and \(N\)-periodic orbits in vector fields
• On the Structure of Spectra of Modulated Travelling Waves
• Using Melnikov's method to solve Silnikov's problems
• Stability of the Travelling Wave Solution of the Fitzhugh-Nagumo System
• ON THE EXISTENCE OF HOMOCLINIC AND PERIODIC ORBITS FOR THE FITZHUGH-NAGUMO EQUATIONS
• The cusp horseshoe and its bifurcations in the unfolding of an inclination-flip homoclinic orbit
• Convergence estimates for the numerical approximation of homoclinic solutions
• Spectral analysis of long wavelength periodic waves and applications.
• Stability of multiple-pulse solutions
• Stability of N-Fronts Bifurcating from a Twisted Heteroclinic Loop and an Application to the Fitzhugh--Nagumo Equation
• Numerical Computation of Solitary Waves in Infinite Cylindrical Domains
• Spectral stability of modulated travelling waves bifurcating near essential instabilities
• Eigenvalues, and instabilities of solitary waves
• Metastable patterns in solutions of u_t = ϵ²u_xx − f(u)
• Stability of Pulses in Nonlinear Optical Fibers Using Phase-Sensitive Amplifiers
• Floquet theory for partial differential equations