313 citations · 730 across the 15 of their papers we have counts for
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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…
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…