Abstract
We consider a lattice equation modelling one-dimensional metamaterials formed by a discrete array of nonlinear resonators. We focus on periodic travelling waves due to the presence of a periodic force. The existence and uniqueness results of periodic travelling waves of the system are presented. Our analytical results are found to be in good agreement with direct numerical computations.
Highlights
In this work, we consider [26] d2 dt2 +γ d dt un un (u2n λu2n−1 λu2n+1)γ d dt u2n h(ωt pn) =
We study the modulational stability of the periodic solutions by computing Floquet multipliers of the linearized systems
We prove the existence of such waves rigorously
Summary
The equation models the dynamics of electromagnetic waves in the so-called magneto-inductive metamaterials. In the lattice equation (1) the nonlinearity appears in the coupling terms and in the damping. This is due to the assumption of the nonlinearity of the capacitance of the split-ring resonators that compose the magneto-inductive materials [26]. Note that in our governing equation (1) the nonlinearity in the coupling terms between the sites is akin to that in the Fermi–Pasta–Ulam lattices [10]. The bifurcation structures of periodic solutions in general FPU lattices forced by periodic drive were studied in [8]. It is imperative to study the effect of the present nonlinear couplings to periodic solutions caused by the same periodic drive. Comparisons with the analytical results are presented where we obtain good agreement
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
