73 citations · 343 across the 31 of their papers we have counts for
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math.AP2010★ 2 cited
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…
math.AP2010★ 24 cited
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…