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.
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Communicated by G. Iooss.
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Herrmann, M. Action Minimising Fronts in General FPU-type Chains. J Nonlinear Sci 21, 33–55 (2011). https://doi.org/10.1007/s00332-010-9075-9
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DOI: https://doi.org/10.1007/s00332-010-9075-9