Destabilization and Localization of Traveling Waves by an Advected Field

Details Destabilization and Localization of Traveling Waves by an Advected Field Destabilization and Localization of Traveling Waves by an Advected Field

2000-09-28

arxiv.org/abs/nlin/0009050v2

Nonlinear Sciences

Pattern Formation and Solitons

23 Pages, 9 Figures

Scientific paper

10.1016/S0167-2789(01)00272-X

{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.

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