Abstract
The bifurcation of wave-like spatio-temporal structures due to a hard-mode instability at non-zero wave number is investigated for a simple class of driven systems in one space dimension. We find generically a bifurcation of two branches of waves, travelling waves and standing waves, characterized by nontrivial subgroups of the symmetry group of the system. If both branches are supercritical, the wave with the larger amplitude is found to be stable. In all other cases, both waves are unstable for small amplitudes. At the common boundary of the stability regions of the two wave types in parameter space we find a bifurcation of a branch of modulated waves involving two independent frequencies, connecting the branches of travelling waves and standing waves.
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Work supported by the Swiss National Science Foundation
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Thiesen, S., Thomas, H. Bifurcation, stability and symmetry of nonlinear waves. Z. Physik B - Condensed Matter 65, 397–408 (1987). https://doi.org/10.1007/BF01303728
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DOI: https://doi.org/10.1007/BF01303728