Exact solutions for discrete breathers in forced-damped chain

TL;DR

This paper derives exact solutions for symmetric discrete breathers in a forced-damped linear chain with vibro-impact constraints, revealing unique stability phenomena and providing analytical and numerical insights.

Contribution

It presents the first analytical derivation of exact discrete breather solutions in a forced-damped vibro-impact chain, including stability analysis.

Findings

Exact solutions for symmetric discrete breathers are obtained.

Unusual non-monotonous stability boundary dependence on forcing amplitude is revealed.

Analytical results are supported by numerical illustrations for small lattices.

Abstract

Exact solutions for symmetric discrete breathers (DBs) are obtained in forced-damped linear chain with on-site vibro-impact constraints. The damping is related to inelastic impacts; the forcing may be chosen from broad class of periodic antisymmetric functions. Global conditions for existence and stability of the DB are established. Some unusual phenomena, like non-monotonous dependence of the stability boundary on the forcing amplitude, are revealed analytically for the full system and illustrated numerically for small periodic lattices.