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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Noncommutative vortices and beach waves

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


Noncommutative vortices and beach waves

Pelinovsky, Kevrekidis, Frantzeskikis 2005


Noncommutative vortices and beach waves

Circular vortex


Noncommutative vortices and beach waves

Peierls-Nabarro potential


Noncommutative vortices and beach waves

Static vortex


Noncommutative vortices and beach waves

Peierls-Nabarro potential


Noncommutative vortices and beach waves

Noncommutative NLS equation


Noncommutative vortices and beach waves

Strominger 2000.


Noncommutative vortices and beach waves

Lindstrom-Rocek 2003


Noncommutative vortices and beach waves

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.


Noncommutative vortices and beach waves

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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