Phase Slips and the Eckhaus Instability

  title={Phase Slips and the Eckhaus Instability},
  author={J Eckmann and Th. Gallay and C. Eugene Wayne},
We consider the Ginzburg-Landau equation, @ t u = @ 2 x u+u?ujuj 2 , with complex amplitude u(x; t). We first analyze the phenomenon of phase slips as a consequence of the local shape of u. We next prove a global theorem about evolution from an Eckhaus unstable state, all the way to the limiting stable finite state, for periodic perturbations of Eckhaus unstable periodic initial data. Equipped with these results, we proceed to prove the corresponding phenomena for the fourth order Swift… CONTINUE READING
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