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The higher-dimensional Ablowitz-Ladik model: from (non-)integrability and solitary waves to surprising collapse properties and more exotic solutions
P. G. Kevrekidis, G. J. Herring, S. Lafortune +1
We propose a consideration of the properties of the two-dimensional Ablowitz-Ladik discretization of the ubiquitous nonlinear Schrodinger (NLS) model. We use singularity confinemen…
Quantization Of Spin Direction For Solitary Waves In A Uniform Magnetic Field
Q. E. Hoq
It is known that there are nonlinear wave equations with localized solitary wave solutions. Some of these solitary waves are stable (with respect to a small perturbation of initial…
Stability of Discrete Solitons in the Presence of Parametric Driving
H. Susanto, Q. E. Hoq, P. G. Kevrekidis
In this brief report, we consider parametrically driven bright solitons in the vicinity of the anti-continuum limit. We illustrate the mechanism through which these solitons become…
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…