Destabilization and Localization of Traveling Waves by an Advected Field

Abstract

{We study a model of small-amplitude traveling waves arising in a supercritical Hopf-bifurcation, that are coupled to a slowly varying, real field. The field is advected by the waves and, in turn, affects their stability via a coupling to the growth rate. In the absence of dispersion we identify two distinct shortwave instabilities. One instability induces a phase slip of the waves and a corresponding reduction of the winding number, while the other leads to a modulated wave structure. The bifurcation to modulated waves can be either forward or backward, in the latter case permitting the existence of localized, traveling pulses which are bistable with the basic, conductive state.

23 Pages, 9 Figures

References in corpus (3)

• Pattern formation with a conservation law
• Localization of Waves without Bistability: Worms in Nematic Electroconvection
• Finite Wavelength Instabilities in a Slow Mode Coupled Complex Ginzburg-Landau Equation

Cited by in corpus (4)

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• Traveling Wave Fronts and Localized Traveling Wave Convection in Binary Fluid Mixtures
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• Tunable front interaction and localization of periodically forced waves