71 citations · 297 across the 17 of their papers we have counts for
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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…