Danish Ph.D. School in Nonlinear Science

Sponsored by the Danish Research Academy

Hamiltonian Description of Nonlinear Waves

by E.A.Kuznetsov
Landau Institute for Theoretical Physics
e-mail: kuznetso@itp.ac.ru

MIDIT-seminar 398

Thursday January 15, 1998, 13.00 h
at MIDIT, IMM Building 305, room 027

Abstract: Hamiltonian description for nonlinear waves in plasma, hydrodynamics and optics will be presented. The main attention will be paid to the problem of canonical variables introducing. The connection with other approaches of the Hamiltonian structure introduction will be ginn, in particular, by means of noncanonical Poisson brackets which are expressed in terms of natuaral variables. The problem of their degeneracy for the ideal hydrodynamics will be discussed in details. It will be shown that the degeneracy is connected with a specific symmetry, i.e., with the so called relabelling group of Lagrangian markers. At the second part of the lecture there will be presented a general method for investigation of weak nonlinear waves based on the classical perturbation theory and reduction of Hamiltonians. It will be shown how using this technique it is possible to get many well-known nonlinear models like the nonlinear Schrodinger equation, the KDV equation, etc.