Gain-loss-driven travelling waves in PT-symmetric nonlinear metamaterials

TL;DR

This paper analyzes the existence of localized travelling waves in PT-symmetric nonlinear magnetic metamaterials using Melnikov analysis, revealing conditions for wave persistence and observing homoclinic snaking phenomena.

Contribution

It introduces an analytical approach to identify conditions for traveling wave solutions in PT-symmetric metamaterials, supported by numerical validation.

Findings

Conditions for homoclinic and heteroclinic orbit persistence.

Good agreement between analytical and numerical results.

Observation of homoclinic snaking in bifurcation diagrams.

Abstract

In this work we investigate a one-dimensional parity-time (PT)-symmetric magnetic metamaterial consisting of split-ring dimers having gain or loss. Employing a Melnikov analysis we study the existence of localized travelling waves, i.e. homoclinic or heteroclinic solutions. We find conditions under which the homoclinic or heteroclinic orbits persist. Our analytical results are found to be in good agreement with direct numerical computations. For the particular nonlinearity admitting travelling kinks, numerically we observe homoclinic snaking in the bifurcation diagram. The Melnikov analysis yields a good approximation to one of the boundaries of the snaking profile.