Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases
Exactly Solvable and Integrable Systems
2013-05-28 v4 Mathematical Physics
math.MP
Abstract
In this paper we examine in detail the procedure of averaging of the local field-theoretic 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 Dubrovin-Novikov procedure. Separate consideration is given to special features of single-phase 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 multi-phase situation.
Cite
@article{arxiv.1203.5732,
title = {Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases},
author = {Andrei Ya. Maltsev},
journal= {arXiv preprint arXiv:1203.5732},
year = {2013}
}
Comments
53 pages, extension to the multi-dimensional case is given in arXiv:1211.5756