The nonlinear magnetoinductive dimer

TL;DR

This paper analyzes a nonlinear magnetoinductive dimer, deriving mode solutions and stability conditions, and demonstrates magnetic energy self-trapping with a coupling-dependent threshold.

Contribution

It provides closed-form solutions for modes and a stability analysis of a nonlinear magnetoinductive dimer, highlighting the always stable asymmetric mode.

Findings

Asymmetric mode is always stable regardless of coupling and nonlinearity type.

Self-trapping of magnetic energy occurs, with a threshold that increases with coupling.

Closed-form solutions for symmetric, antisymmetric, and asymmetric modes are derived.

Abstract

We examine a nonlinear magnetoinductive dimer and compute its linear and nonlinear symmetric, antisymmetric and asymmetric modes in closed-form, in the rotating-wave approximation. A linear stability analysis of these modes reveals that the asymmetric mode is always stable, for any allowed value of the coupling parameter and for both, hard and soft nonlinearity. A numerical computation of the dimer dynamics reveals a magnetic energy selftrapping whose threshold increases for increasing dimer coupling.