108 citations · 556 across the 36 of their papers we have counts for
8 papers · 1 filter
Discrete solitons and vortices in hexagonal and honeycomb lattices: Existence, stability, and dynamics
K. J. H. Law, P. G. Kevrekidis, V. Koukouloyannis +3
We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schroedinger equation on nonsquare lattice geometries. We present a systematic classification of…
Discrete Breathers in Two-Dimensional Anisotropic Nonlinear Schrodinger lattices
J. Gomez-Gardenes, L. M. Floria, A. R. Bishop
We study the structure and stability of discrete breathers (both pinned and mobile) in two-dimensional nonlinear anisotropic Schrodinger lattices. Starting from a set of identical…
Discrete Solitons in the Salerno Model with competing nonlinearities
J. Gomez-Gardenes, B. A. Malomed, L. M. Floria +1
We consider a lattice equation (Salerno model) combining onsite self-focusing and intersite self-defocusing cubic terms, which may describe a Bose-Einstein condensate of dipolar at…
Statics and Dynamics of an Inhomogeneously-Nonlinear Lattice
Debra L. Machacek, Elizabeth A. Foreman, Q. E. Hoq +4
We introduce an inhomogeneously-nonlinear Schr{ö}dinger lattice, featuring a defocusing segment, a focusing segment and a transitional interface between the two. We illustrate that…
Asymptotic Calculation of Discrete Nonlinear Wave Interactions
P. G. Kevrekidis, Avinash Khare, A. Saxena +2
We illustrate how to compute asymptotic interactions between discrete solitary waves of dispersive equations, using the approach proposed by Manton [Nucl. Phys. B 150, 397 (1979)].…
Localization of nonlinear excitations in curved waveguides
Yu. B. Gaididei, P. L. Christiansen, P. G. Kevrekidis +2
Motivated by the example of a curved waveguide embedded in a photonic crystal, we examine the effects of geometry in a ``quantum channel'' of parabolic form. We study the linear ca…