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We propose an approach for constructing asymmetric nested lattice samples by randomizing asymmetric nested orthogonal arrays. Such designs possess a desirable nested structure and have attractive spac...
We investigate the dynamics of vortices in repulsive Bose–Einstein condensates in the presence of an optical lattice (OL) and a parabolic magnetic trap. The dynamics is sensitive to the phase of the O...
We investigate the stability of dark solitons (DSs) in an effectively one-dimensional Bose-Einstein condensate in the presence of the magnetic parabolic trap and an optical lattice (OL). The analysis ...
We investigate the dynamics of vortices in repulsive Bose–Einstein condensates in the presence of an optical lattice (OL) and a parabolic magnetic trap. The dynamics is sensitive to the phase of the O...
We obtain an exact solution for the breather lattice solution of the modified Korteweg–de Vries equation. Numerical simulation of the breather lattice demonstrates its instability due to the breather-...
We examine collisions between identical solitons in a weakly perturbed Ablowitz-Ladik (AL) model, augmented by either onsite cubic nonlinearity (which corresponds to the Salerno model, and may be real...
In a benchmark dynamical-lattice model in three dimensions, the discrete nonlinear Schrödinger equation, we find discrete vortex solitons with various values of the topological charge S. Stabilit...
We introduce a notion of balanced configurations of vectors. This is motivated by the study of rational A-hypergeometric functions in the sense of Gelfand, Kapranov and Zelevinsky. We classify balance...
The Fermi–Pasta–Ulam (FPU) model, which was proposed 50 years ago to examine thermalization in nonmetallic solids and develop “experimental” techniques for studying nonlinear problems, continues...
We give large deviation upper bounds, and discuss lower bounds, for the Gibbs-KMS state of a system of quantum spins or an interacting Fermi gas on the lattice. We cover general interactions and gener...
A theory of the nonsymmetric Landau-Zener tunneling of Bose-Einstein condensates in deep optical lattices is presented. It is shown that periodic exchange of matter between the bands is described by a...
We introduce an inhomogeneously nonlinear Schrödinger lattice, featuring a defocusing segment, a focusing segment and a transitional interface between the two. We illustrate that such inhomogeneo...
Let P be a simple lattice polytope. We define an action of the Hecke operators on E(P), the Ehrhart polynomial of P, and describe their effect on the coefficients of E(P). We also describe how the Bri...
We investigate the existence and especially the linear stability of single- and multiple-charge quantized vortex states of nonlinear Schrödinger equations in the presence of a periodic and a para...
In this work, we study two-dimensional Bose–Einstein condensates confined by both a cylindrically symmetric harmonic potential and an optical lattice with equal periodicity in two orthogonal direction...

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