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

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

2000-10-20

arxiv.org/abs/nlin/0010035v1

Nonlinear Sciences

Pattern Formation and Solitons

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

Scientific paper

10.1103/PhysRevE.62.7802

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.

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