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

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.