
SIGMA 8 (2012), 103, 54 pages arXiv:1203.5732
https://doi.org/10.3842/SIGMA.2012.103
Contribution to the Special Issue “Geometrical Methods in Mathematical Physics”
Whitham's Method and DubrovinNovikov Bracket in SinglePhase and Multiphase Cases
Andrei Ya. Maltsev
L.D. Landau Institute for Theoretical Physics, 1A Ak. Semenova Ave., Chernogolovka, Moscow reg., 142432, Russia
Received April 23, 2012, in final form December 11, 2012; Published online December 24, 2012
Abstract
In this paper we examine in detail the procedure of averaging
of the local fieldtheoretic Poisson brackets proposed by B.A. Dubrovin
and S.P. Novikov for the method of Whitham.
The main attention is paid to
the questions of justification and the conditions of applicability of the
DubrovinNovikov procedure.
Separate consideration is given to special
features of singlephase and multiphase cases.
In particular, one of the
main results is the insensitivity of the procedure of bracket averaging
to the appearance of ''resonances'' which can arise in the multiphase
situation.
Key words:
quasiperiodic solutions; slow modulations; Hamiltonian structures.
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