Abstract

Evolution of the Periodic Perturbations in Absolutely Unstable Media

A.V.Aksenov (Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia)

e-mail: aksenov@mech.math.msu.su

The system of the equations for describing small long wavelength perturbations in the absolutely unstable media is considered. Symmetries and invariant solutions of this equations are presented. It was shown that the periodic solutions of this equations are the fundamental solutions of the Euler--Poisson--Darboux equation. The invariant and different fundamental solutions of the Euler--Poisson--Darboux equation are found. Final studies of the evolution of the periodic perturbations in absolutely unstable media are investigated.

Section : 12