Action minimizing fronts in general FPU-type chains

TL;DR

This paper proves the existence of action-minimizing heteroclinic traveling wave fronts in nonlinear atomic chains with non-convex potentials, extending previous results to non-monotone profiles and providing numerical validation.

Contribution

It generalizes recent work by allowing non-convex interaction potentials and non-monotone wave profiles, establishing conditions for front existence in FPU-type chains.

Findings

Existence of heteroclinic traveling wave fronts under new conditions.

Front profiles can be non-monotone in non-convex potentials.

Numerical simulations support theoretical results.

Abstract

We study atomic chains with nonlinear nearest neighbour interactions and prove the existence of fronts (heteroclinic travelling waves with constant asymptotic states). Generalizing recent results of Herrmann and Rademacher we allow for non-convex interaction potentials and find fronts with non-monotone profile. These fronts minimize 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.