Berry phases in the reconstructed KdV equation

8Citations
Citations of this article
6Readers
Mendeley users who have this article in their library.
Get full text

Abstract

We consider the KdV equation on a circle and its Lie-Poisson reconstruction, which is reminiscent of an equation of motion for fluid particles. For periodic waves, the stroboscopic reconstructed motion is governed by an iterated map whose Poincaré rotation number yields the drift velocity. We show that this number has a geometric origin: it is the sum of a dynamical phase, a Berry phase, and an "anomalous phase."The last two quantities are universal: they are solely due to the underlying Virasoro group structure. The Berry phase, in particular, was previously described by Oblak [J. High Energy Phys. 10, 114 (2017)] for two-dimensional conformal field theories and follows from adiabatic deformations produced by the propagating wave. We illustrate these general results with cnoidal waves, for which all phases can be evaluated in closed form thanks to a uniformizing map that we derive. Along the way, we encounter "orbital bifurcations"occurring when a wave becomes non-uniformizable: there exists a resonance wedge, in the cnoidal parameter space, where particle motion is locked to the wave, while no such locking occurs outside of the wedge.

Cite

CITATION STYLE

APA

Oblak, B., & Kozyreff, G. (2020). Berry phases in the reconstructed KdV equation. Chaos, 30(11). https://doi.org/10.1063/5.0021892

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free