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.

12 pages

References in corpus (5)

• Nonlinear properties of left-handed metamaterials
• Tunable split-ring resonators for nonlinear negative-index metamaterials
• Self-focusing and envelope pulse generation in nonlinear magnetic metamaterials
• Nonlinear magnetoinductive waves and domain walls in composite metamaterials
• Stability of Discrete Solitons in the Presence of Parametric Driving

Cited by in corpus (2)

• Travelling waves in nonlinear magneto-inductive lattices
• Low-power threshold gas discharge by enhanced local electric field in electromagnetically-induced-transparencylike metamolecules