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Bifurcation results for traveling waves in nonlinear magnetic metamaterials. (English) Zbl 1304.34084

Summary: 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.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
78A48 Composite media; random media in optics and electromagnetic theory
34B40 Boundary value problems on infinite intervals for ordinary differential equations
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