Essential instability of pulses and bifurcations to modulated travelling waves

DOI10.1017/S0308210500019387zbMath0956.35065OpenAlexW2053959672MaRDI QIDQ4935383

Björn Sandstede, Arnd Scheel

Publication date: 28 February 2001

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500019387

zbMATH Keywords

bifurcation of a family of large patternsessential spectrum of the linearizationreaction-diffusion systems on real line

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Bifurcations in context of PDEs (35B32) Initial value problems for second-order parabolic systems (35K45)

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Cites Work

• Bifurcation of singular solutions in reversible systems and applications to reaction-diffusion equations
• A reduction principle for nonautonomous systems in infinite-dimensional spaces
• Singularities and groups in bifurcation theory. Volume I
• Geometric theory of semilinear parabolic equations
• Dichotomies in stability theory
• Bifurcating time-periodic solutions of Navier-Stokes equations in infinite cylinders
• Exponential dichotomies for solitary-wave solutions of semilinear elliptic equations on infinite cylinders
• The time dependent amplitude equation for the Swift-Hohenberg problem
• Wave-solutions of reversible systems and applications
• Exponential dichotomies and transversal homoclinic points
• Invading wave fronts and their oscillatory wakes are linked by a modulated travelling phase resetting wave
• Pulse Dynamics in an Unstable Medium
• Stability of multiple-pulse solutions
• Stability of N-Fronts Bifurcating from a Twisted Heteroclinic Loop and an Application to the Fitzhugh--Nagumo Equation
• The chemical basis of morphogenesis
• Attractors for modulation equations on unbounded domains-existence and comparison