71 citations · 180 across the 11 of their papers we have counts for
9 papers · 1 filter
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…
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…
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…