Frontiers in Nonlinear Waves
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Frontiers in Nonlinear Waves in 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.

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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


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