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

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. •A one-dimensional model of nonlinear magnetic metamaterials with parity-time-symmetric potentials is considered.•The existence of localized travelling waves is obtained by performing a Melnikov function analysis.•Direct numerical computations are performed showing good agreement with the analysis.•A snaking structure in the bifurcation diagram can be obtained.