73 citations · 343 across the 31 of their papers we have counts for
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Vortex Collapse for the L2-Critical Nonlinear Schrödinger Equation
Gideon Simpson, Ian Zwiers
The focusing cubic nonlinear Schrödinger equation in two dimensions admits vortex solitons, standing wave solutions with spatial structure, Qm(r,theta) = e^{i m theta} Rm(r). In th…
Coherent Structures and Carrier Shocks in the Nonlinear Periodic Maxwell Equations
Gideon Simpson, Michael I. Weinstein
We consider the one-dimensional propagation of electromagnetic waves in a weakly nonlinear and low-contrast spatially inhomogeneous medium with no energy dissipation. We focus on t…
Solitary Wave Benchmarks in Magma Dynamics
Gideon Simpson, Marc Spiegelman
We present a model problem for benchmarking codes that investigate magma migration in the Earth's interior. This system retains the essential features of more sophisticated models,…
Spectral Analysis for Matrix Hamiltonian Operators
Jeremy L. Marzuola, Gideon Simpson
In this work, we study the spectral properties of matrix Hamiltonians generated by linearizing the nonlinear Schrödinger equation about soliton solutions. By a numerically assisted…