Asymptotic solutions of pseudodifferential wave equations

Details Asymptotic solutions of pseudodifferential wave equations Asymptotic solutions of pseudodifferential wave equations

2004-11-10

arxiv.org/abs/math-ph/0411039v1

Physics

Mathematical Physics

Proceedings of the Joint Varenna-Lausanne International Workshop on "Theory of Fusion Plasmas", Varenna 2004

Scientific paper

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.

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