Discrete Electrical Lattice Research Articles

Gap Soliton Modes in an Electrical Lattice

We study analytically by a quasi-discreteness approach, nonlinear localized excitations in a discrete electrical lattice which exhibits two natural gaps. We show that some new types of gap solitons as well as intrinsic localized modes, both waves having a zero-group velocity can exist in the line. These nonlinear excitations have also their frequency lying in the gaps of the continuous wave spectrum and oscillate with frequency being above all the phonon bands, respectively.

Spatially localized voltage oscillations in an electrical lattice

A quasi-discreteness approximation is employed to study analytically spatially localized voltage oscillations in a discrete electrical lattice. We show that the system may support new types of gap solitons as well as upper cut-off solitons (intrinsic localized modes), both nonlinear localized modes having a zero group velocity.

Observation of nonlinear localized modes in an electrical lattice.

We study a discrete electrical lattice where the dynamics of modulated waves can be modeled by a generalized discrete nonlinear Schr\"odinger equation that interpolates between the Ablowitz-Ladik and discrete-self-trapping equations. Regions of modulational instability (MI) are investigated and experimentally, we observe that MI can develop even for continuous waves with frequencies higher than the linear cutoff frequency of the lattice. These results are confirmed by the observation of ``staggered'' localized modes. Experimentally, it is finally shown that unlike envelope solitons, which can be observed close to the zero-dispersion point, the staggered modes experience strong lattice effects.