Bifurcation Results for Traveling Waves in Nonlinear Magnetic Metamaterials

Abstract

In this work, we study a model of a one-dimensional magnetic metamaterial formed by a discrete array of nonlinear resonators. We focus on periodic and localized traveling waves of the model, in the presence of loss and an external drive. Employing a Melnikov analysis we study the existence and persistence of such traveling waves, and study their linear stability. We show that, under certain conditions, the presence of dissipation and/or driving may stabilize or destabilize the solutions. Our analytical results are found to be in good agreement with direct numerical computations.

arXiv comment12 pages

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Cited by in corpus (3)

• Travelling waves in nonlinear magneto-inductive lattices
• Frequency mixing at an electromagnetically induced transparency like metasurface loaded with gas as a nonlinear element
• Low-power threshold gas discharge by enhanced local electric field in electromagnetically-induced-transparencylike metamolecules