Ground waves in atomic chains with bi-monomial double-well potential

TL;DR

This paper proves the existence of periodic and solitary ground waves in atomic chains with a bi-monomial double-well potential, using variational methods and numerical computations.

Contribution

It introduces a new variational approach to establish the existence of ground waves in FPU-type chains with double-well potentials and demonstrates their convergence.

Findings

Existence of periodic and solitary ground waves proven mathematically.

Numerical computation of ground waves via discretized gradient flow.

Periodic ground waves converge to solitary waves.

Abstract

Ground waves in atomic chains are traveling waves that corresponds to minimal non-trivial critical values of the underlying action functional. In this paper we study FPU-type chains with bi-monomial double-well potential and prove the existence of both periodic and solitary ground waves. To this end we minimize the action on the Nehari manifold and show that periodic ground waves converge to solitary ones. Finally, we compute ground waves numerically by a suitable discretization of a constrained gradient flow.