ABSTRACT
We study numerically a parametrically driven discrete nonlinear Schrödinger equation modeling periodically curved waveguide arrays. We show that discrete surface solitons persist, but their threshold power is altered by the drive. There are critical drives at which the threshold values vanish. We also show that parametric drives can create resonance with a phonon making a barrier for discrete solitons. By calculating the corresponding Floquet multipliers, we find that the stability of symmetric and antisymmetric off-side discrete surface solitons switches approximately at the critical drives for thresholdless solitons.
ABSTRACT
We present the results of a numerical investigation of the Ericksen-Leslie equations for the problem of electrohydrodynamic convection in a nematic liquid crystal. The combination of a finite element approach and numerical bifurcation techniques allows us to provide details of the basic flow and include the physically relevant effect of nonslip side walls. We are also able to include material properties as parameters and this permits us to draw comparisons with available experimental data. We then compare and contrast the bifurcation structure with that of Rayleigh-Bénard and Taylor-Couette flows and explore the role of symmetries by including a fringing electric field.
