60 citations · 137 across the 27 of their papers we have counts for
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Stability of closed solutions to the VFE hierarchy with application to the Hirota equation
Thomas Ivey, Stephane Lafortune
The Vortex Filament Equation (VFE) is part of an integrable hierarchy of filament equations. Several equations part of this hierarchy have been derived to describe vortex filaments…
Integrable Flows for Starlike Curves in Centroaffine Space
Annalisa Calini, Thomas Ivey, Gloria Mari Beffa
We construct integrable hierarchies of flows for curves in centroaffine through a natural pre-symplectic structure on the space of closed unparametrized starlike cu…
Remarks on KdV-type Flows on Star-Shaped Curves
Annalisa Calini, Thomas Ivey, Gloria Mari Beffa
We study the relation between the centro-affine geometry of star-shaped planar curves and the projective geometry of parametrized maps into $\RP^1$. We show that projectivization i…
Spectral stability of periodic NLS and CGL solutions
Thomas Ivey, Stephane Lafortune
We consider periodic traveling wave solutions to the focusing nonlinear Schrodinger equation (NLS) that have been shown to persist when the NLS is perturbed to the complex Ginzburg…
Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations
Annalisa M. Calini, Thomas A. Ivey
We study the topology of quasiperiodic solutions of the vortex filament equation in a neighborhood of multiply covered circles. We construct these solutions by means of a sequence…
Finite-gap Solutions of the Vortex Filament Equation, I
Annalisa Calini, Thomas Ivey
For the class of quasi-periodic solutions of the vortex filament equation, we study connections between the algebro-geometric data used for their explicit construction and the geom…