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Noncommutative vortices and beach waves

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Frontiers in Nonlinear Wavesin honor of Vladimir Zakharov's 70th birthday

Noncommutative vortices and beach waves

G. Cruz

L.R. Juárez

A. A. Minzoni

M. Rosenbaum

IIMAS-FENOMEC, UNAM

Pelinovsky, Kevrekidis, Frantzeskikis 2005

Circular vortex

Peierls-Nabarro potential

Static vortex

Peierls-Nabarro potential

Noncommutative NLS equation

Strominger 2000.

Lindstrom-Rocek 2003

Modulation equations

The last expression is the equation of motion for the peak of the vortex, analogous to a particle in a Peierls-Nabarro potential.

Large vortex with low energy

The vortex moves in the lattice generated by the *-product.

The fixed points are the equilibrium positions