Solitons and vortices in honeycomb defocusing photonic lattices (2008)
Law, K. J. H., Susanto, H., Kevrekidis, P. G.
Solitons and necklaces in the first band-gap of a two-dimensional optically induced honeycomb defocusing photonic lattice are theoretically considered. It is shown that dipoles, soliton necklaces,...
Vortex solutions of the discrete Gross-Pitaevskii equation (2008)
Cuevas, J., James, G., Kevrekidis, P. G., Law, K. J. H.
In this paper, we consider the dynamical evolution of dark vortex states in the two-dimensional defocusing discrete nonlinear Schroedinger model, a model of interest both to atomic physics and to...
Law, K. J. H., Kevrekidis, P. G., Anderson, B. P., Carretero-Gonzalez, R., Frantzeskakis, D. J.
In this work, we study pancake-shaped Bose-Einstein condensates confined by both a cylindrically symmetric harmonic potential and an optical lattice with equal periodicity in two orthogonal...
Stability of Quantized Vortices in a Bose-Einstein Condensate Confined in an Optical Lattice (2008)
Law, K. J. H., Qiao, L., Kevrekidis, P. G., Kevrekidis, I. G.
We investigate the existence and especially the linear stability of single and multiple-charge quantized vortex states of nonlinear Schroedinger equations in the presence of a periodic and a...
Averaging of Nonlinearity Management with Dissipation (2008)
Beheshti, S., Law, K. J. H., Kevrekidis, P. G., Porter, Mason A.
Motivated by recent experiments in optics and atomic physics, we derive an averaged nonlinear partial differential equation describing the dynamics of the complex field in a nonlinear Schroedinger...
Law, K. J. H., Kevrekidis, P. G., Frantzeskakis, D. J., Bishop, A. R.
Motivated by recent work on instabilities in expanding domains in reaction-diffusion settings, we propose an analog of such mechanisms in energy-conserving wave equations. In particular, we consider...