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Mardi 2 février, 2021 - 14:00

Berry Phases and Drift in the KdV Equation

Blagoje Oblak (LPTHE, Sorbonne) - en visio

par Revaz Ramazashvili - 2 février 2021

I consider a model of fluid particle motion closely related to the Korteweg-de Vries equation governing shallow water dynamics. Using the reformulation of this model as a geodesic in an infinite-dimensional group, the drift velocity of particles is shown to be an ergodic rotation number, sensitive to Berry phases produced by adiabatic spatial deformations. Along the way, I show that the topology of coadjoint orbits of wave profiles affects drift in a dramatic manner : orbits that are not homotopic to a point yield quantized rotation numbers. These arguments rely on the general structure of Euler equations, suggesting the existence of other similar applications of infinite-dimensional geometry to nonlinear waves.

Post-scriptum :

contact : B. Georgeot