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Anatoly Kamchatnov

2008-03-05
15:30:00 - 17:20:00

Physics and mathematics of dispersive shocks: An introduction

405 , Mathematics Research Center Building (ori. New Math. Bldg.)

In the first part of this lecture, we shall study dispersion effects in evolution of wave packets. The notions of "group velocity" and "parabolic equation" will be introduced. From the fact that wave packets spread out with time, we conclude that nonlinear effects should be taken into account for explanation of dispersive shocks. In the second part of the lecture we shall start studying effects of nonlinearity on wave evolution. Wave breaking phenomenon will be explained first in the simplest case of Hopf equation and then it will be generalized on so called "simple waves" solution of compressible gas dynamics equations. This solution will be illustrated by itsapplication to "piston problem".