71 citations · 297 across the 17 of their papers we have counts for
18 papers
Spiral Wave Solutions in Water Waves
Mark J. Ablowitz, Justin T. Cole, Sean D. Nixon
Spiral wave solutions are found in linear and weakly nonlinear irrotational water wave equations. These unsteady spiral waves evolve from suitable initial conditions; they are not…
Collapse dynamics for two-dimensional space-time nonlocal nonlinear Schrodinger equations
Justin T. Cole, Abdullah M. Aurko, Ziad H. Musslimani
The question of collapse (blow-up) in finite time is investigated for the two-dimensional (non-integrable) space-time nonlocal nonlinear Schrodinger equations. Starting from the tw…
The Haldane Model in a Magneto-optical Honeycomb Lattice
M. J. Ablowitz, J. T. Cole
A two-dimensional honeycomb lattice composed of gyrotropic rods is studied. Beginning with Maxwell's equations, a perturbed Wannier method is introduced which yields a tight-bindin…
Switching via Wave Interaction in Topological Photonic Lattices
Mark J. Ablowitz, Justin T. Cole, S. D. Nixon
A honeycomb Floquet lattice with helically rotating waveguides and an interface separating two counter-propagating subdomains is analyzed. Two topologically protected localized wav…
Nonlinear optical waveguide lattices: Asymptotic analysis, solitons, and topological insulators
Mark J. Ablowitz, Justin T. Cole
In recent years, there has been considerable interest in the study of wave propagation in nonlinear photonic lattices. The interplay between nonlinearity and periodicity has led re…
Soliton-mean field interaction in Korteweg-de Vries dispersive hydrodynamics
Mark J. Ablowitz, Justin T. Cole, Gennady A. El +2
The propagation of localized solitons in the presence of large-scale waves is a fundamental problem, both physically and mathematically, with applications in fluid dynamics, nonlin…
Unified approach to Floquet lattices, topological insulators, and their nonlinear dynamics
Mark Ablowitz, Justin T. Cole, Sean Nixon
A unified method to analyze the dynamics and topological structure associated with a class of Floquet topological insulators is presented. The method is applied to a system that de…
On the Whitham system for the (2+1)-dimensional nonlinear Schrödinger equation
Mark J. Ablowitz, Justin T. Cole, Igor Rumanov
We derive the Whitham modulation equations for the nonlinear Schrödinger equation in the plane (2d NLS) with small dispersion. The modulation equations are derived in terms of both…
Transverse Instability of Rogue Waves
Mark J. Ablowitz, Justin T. Cole
Rogue waves are abnormally large waves which appear unexpectedly and have attracted considerable attention, particularly in recent years. The one space, one time (1+1) nonlinear Sc…
Peierls-Nabarro barrier effect in nonlinear Floquet topological insulators
Mark J. Ablowitz, Justin T. Cole, Pipi Hu +1
The Peierls-Nabarro barrier is a discrete effect that frequently occurs in discrete nonlinear systems. A signature of the barrier is the slowing and eventual stopping of discrete s…
Whitham equations and phase shifts for the Korteweg-deVries equation
Mark J. Ablowitz, Justin T. Cole, Igor Rumanov
The semi-classical Korteweg-deVries equation for step-like data is considered with a small parameter in front of the highest derivative. Using perturbation analysis Whitham theory…
Discrete Approximation of Topologically Protected Modes in Magneto-Optical Media
Mark J. Ablowitz, Justin T. Cole
Topologically protected waves in the linearly polarized Maxwell's equations with gyrotropic, magneto-optic media were studied a decade ago both computationally and experimentally.…
Stellar Kinematics and Environment at z~0.8 in the LEGA-C Survey: Massive, Slow-Rotators are Built First in Overdense Environments
Justin Cole, Rachel Bezanson, Arjen van der Wel +11
In this letter, we investigate the impact of environment on integrated and spatially-resolved stellar kinematics of a sample of massive, quiescent galaxies at intermediate redshift…
On the Whitham system for the radial nonlinear Schrödinger equation
Mark J. Ablowitz, Justin T. Cole, Igor Rumanov
Dispersive shock waves (DSWs) of the defocusing radial nonlinear Schrödinger (rNLS) equation in two spatial dimensions are studied. This equation arises naturally in Bose-Einstein…
Topological insulators in longitudinally driven waveguides: Lieb and Kagome lattices
Mark J. Ablowitz, Justin T. Cole
Topological insulators are studied via tight-binding approximations of longitudinally driven photonic lattices with three lattice sites per unit cell. Two cases are considered in d…
Solitons, the Korteweg-de Vries equation with step boundary values and pseudo-embedded eigenvalues
Mark J. Ablowitz, Xu-Dan Luo, Justin T. Cole
The Korteweg-deVries (KdV) equation with step boundary conditions is considered, with an emphasis on soliton dynamics. When one or more initial solitons are of sufficient size they…
Tight-binding methods for general longitudinally driven photonic lattices -- edge states and solitons
Mark J. Ablowitz, Justin T. Cole
A systematic approach for deriving tight-binding approximations in general longitudinally driven lattices is presented. As prototypes, honeycomb and staggered square lattices are c…
Time-dependent spectral renormalization method
Justin T. Cole, Ziad H. Musslimani
The spectral renormalization method was introduced by Ablowitz and Musslimani in 2005, [Opt. Lett. 30, pp. 2140-2142] as an effective way to numerically compute (time-independent)…