Noncommutative vortices and beach waves

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Noncommutative vortices and beach waves G. Cruz L.R. Juárez A. A. Minzoni M. Rosenbaum IIMAS-FENOMEC, UNAM Frontiers in Nonlinear Waves in honor of Vladimir Zakharov's 70th birthday

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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. - PowerPoint PPT Presentation

Transcript of Noncommutative vortices and beach waves

Page 1: Noncommutative vortices and beach waves

Noncommutative vortices and beach waves

G. Cruz

L.R. Juárez

A. A. Minzoni

M. Rosenbaum

IIMAS-FENOMEC, UNAM

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

Page 2: Noncommutative vortices and beach waves

Pelinovsky, Kevrekidis, Frantzeskikis 2005

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Circular vortex

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Peierls-Nabarro potential

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Static vortex

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Peierls-Nabarro potential

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Noncommutative NLS equation

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Strominger 2000.

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Page 11: Noncommutative vortices and beach waves

Lindstrom-Rocek 2003

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Page 13: 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.

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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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