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…