Wigner dynamics and limit of geometrical optics in inhomogeneous dispersive media

Omar Morandi

doi:10.3934/krm.2024012

Article Contents

2025, Volume 18, Issue 1: 76-100. Doi: 10.3934/krm.2024012

This issue Previous Article Well-posedness and trend to equilibrium for the Vlasov-Poisson-Fokker-Planck system with a confining potential Next Article Asymptotic behavior of the two-dimensional Vlasov-Poisson-Fokker-Planck equation with a strong external magnetic field

Wigner dynamics and limit of geometrical optics in inhomogeneous dispersive media

Omar Morandi

University of Florence, Department of Mathematics and Informatics, Italy

Received: July 2023

Revised: February 2024

Early access: April 16, 2024

Published online: April 16, 2024

The work has been developed under the auspices of GNFM (INdAM).

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Abstract

We study the limit of geometrical optics in dispersive inhomogeneous media. The short wavelength regime of the wave equation is investigated in the framework of the Wigner quasi-distribution function in the phase-space. The evolution of the field is expressed by a Cauchy problem for the position and direction of the optical rays. The extended time-frequency phase-space formalism furnishes a natural framework to study the fast oscillating limit of fields governed by non local in time pseudo-differential equations.

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Mathematics Subject Classification: Primary: 81S30, 78A05, 82C70; Secondary: 35S10, 78M35.

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