Starting from the Burton-Cabrera-Frank model in the presence of electromigration, we derive a nonlinear continuum version of step dynamics, where steps undergo a bunching instability. The obtained equation for the steps density is a mixture of the Korteweg-de Vries equation, which leads to solitons, and the Burger equation, which exhibits spatiotemporal chaos. For a small dispersive term, spatiotemporal chaotic pulses prevail. On increasing this term, we observe gradually a transition towards regular pulses.
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Misbah et al. (1996) studied this question.
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