313 citations · 2k across the 51 of their papers we have counts for
53 papers
Topological routing in Chern insulators
Mark J. Ablowitz, Justin T. Cole, Sean D. Nixon
Chern insulator systems are realizable in numerous physical systems and can support robust nonreciprocal transmission of energy. A routing functionality constructed from two counte…
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…
On the integrable six-wave interaction system and its space-time shifted reduction
Mark J. Ablowitz, Ramesh Gupta, Ziad H. Musslimani +1
The multi-dimensional six-wave interaction system is derived in the context of nonlinear optics. Starting from Maxwell's equations, a reduced system of equations governing the dyna…
Inverse scattering transform for continuous and discrete space-time shifted integrable equations
Mark J. Ablowitz, Ziad H. Musslimani, Nicholas J. Ossi
Nonlocal integrable partial differential equations possessing a spatial or temporal reflection have constituted an active research area for the past decade. Recently, more general…
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…