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Anatoly Kamchatnov

2008-04-30
15:30:00 - 17:20:00

Physics and mathematics of dispersive shocks: An introduction

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

In this lecture, we will shall show that the KdV hierarchy has a Hamiltonian structure and all Hamiltonians commute with each other with respect to the Poisson bracket. This leads to notion of complete integrability of the KdV hierarchy equations. After that, we shall give a few simple applications of the developed theory: (1) derivation of periodic solutions (2) new simple derivation of Whitham equations (3) cnoidal wave solution of the whole hierarchy (4) Whitham equations for higher KdV equations.