Bifurcation of travelling waves in implicit nonlinear lattices: applications in metamaterials

Abstract

We consider implicit nonlinear lattice equations modelling one-dimensional metamaterials formed by a discrete array of nonlinear split-ring resonators. We study the existence and bifurcation of localised excitations and use the results to prove the existence of periodic travelling waves in the presence of small damping and travelling drive. Two different systems are considered, with each of them admitting either homoclinic or heteroclinic solutions.

Keywords:

• Lattices
• metamaterials
• periodic and localised solutions

AMS Subject Classifications:

• 34C25
• 34C37

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

MF is partially supported by [grant number VEGA-MS 1/0071/14], [grant number VEGA-SAV 2/0029/13] and by the Slovak Research and Development Agency under the contract No. [APVV-14-0378]. MP is supported by [grant number VEGA-SAV 2/0029/13].