Action Minimising Fronts in General FPU-type Chains
Abstract
We study atomic chains with nonlinear nearest neighbour interactions and prove the existence of fronts (heteroclinic travelling waves with constant asymptotic states). Generalising recent results of Herrmann and Rademacher we allow for non-convex interaction potentials and find fronts with non-monotone profile. These fronts minimise an action integral and can only exists if the asymptotic states fulfil the macroscopic constraints and if the interaction potential satisfies a geometric graph condition. Finally, we illustrate our findings by numerical simulations.
- Publication:
-
Journal of NonLinear Science
- Pub Date:
- February 2011
- DOI:
- 10.1007/s00332-010-9075-9
- arXiv:
- arXiv:1002.0263
- Bibcode:
- 2011JNS....21...33H
- Keywords:
-
- Fermi–Pasta–Ulam chain;
- Heteroclinic travelling waves;
- Conservative shocks;
- Least action principle;
- 37K60;
- 47J30;
- 70F45;
- 74J30;
- Mathematics - Dynamical Systems;
- Mathematical Physics;
- 37K60;
- 47J30;
- 70F45;
- 74J30
- E-Print:
- 19 pages, several figures