Retracting fronts for the nonlinear complex heat equation

Abstract

The "nonlinear complex heat equation" $A_t=i|A{|}^{2}A+A_{xx}$ was introduced by P. Coullet and L. Kramer as a model equation exhibiting travelling fronts induced by non-variational effects, called "retracting fronts". In this paper we study the existence of such fronts. They go by one-parameter families, bounded at one end by the slowest and "steepest" front among the family, a situation presenting striking analogies with front propagation into unstable states.

21 pages, 6 figures