Whitham's method and Dubrovin - Novikov bracket in single-phase and multiphase cases

Details Whitham's method and Dubrovin - Novikov bracket in single-phase and multiphase cases Whitham's method and Dubrovin - Novikov bracket in single-phase and multiphase cases

2012-03-26

arxiv.org/abs/1203.5732v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

62 pages, latex

Scientific paper

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.

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