Emergence of Approximate Translation Invariance in Finite Intervals as a Speed Selection Mechanism for Propagating Fronts

Abstract

We introduce a new velocity selection criterion for fronts propagating into unstable and metastable states. We restrict these fronts to large finite intervals in the comoving frame of reference and require their centers be insensitive to the locations of the ends of the finite intervals, exhibiting thus effectively an approximate translation invariance. Only one monotonic front has this behavior and its velocity is the one that is physically selected. We present analytic results in the case of piecewise parabolic potentials, and numerical results in other cases.

11 pages LaTex with 3 Postscipt Figures. To appear in Physical Review E

References in corpus (1)

• Shift in the velocity of a front due to a cut-off

Cited by in corpus (2)

• Front propagation into unstable states
• Speed Selection Mechanism for Propagating Fronts in Reaction-Diffusion Systems with Multiple Fields