Asymptotic solutions of pseudodifferential wave equations

TL;DR

This paper explores the use of pseudodifferential calculus to derive asymptotic solutions for high-frequency wave equations, focusing on electromagnetic waves in plasma and emphasizing paraxial Gaussian wave propagation.

Contribution

It demonstrates the application of pseudodifferential operators to solve linear wave equations in plasma physics and discusses the uniqueness of the dispersion tensor for these asymptotic solutions.

Findings

Pseudodifferential operators effectively model plasma wave propagation.

Asymptotic techniques yield solutions for paraxial Gaussian waves.

The dispersion tensor is shown to be unique in this context.

Abstract

The aim of this paper is to give an account of some applications of pseudodifferential calculus for solving linear wave equations in the limit of high frequency/short wavelength waves. More specifically, on using as a benchmark the case of electromagnetic waves propagating in a cold isotropic slowly space- and time-varying plasma, it is shown that, in general, linear plasma waves are governed by pseudodifferential operators. Thereafter, the asymptotic techniques for solving the corresponding pseudodifferential wave equations are presented with emphasis on the paraxial propagation of Gaussian wave trains in a cold isotropic plasma. Finally, it is addressed the unicity of the dispersion tensor in terms of which the considered asymptotic solutions are determined.