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
Moscow
Russia
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.