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

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 p...

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Main Author: Andrei Ya. Maltsev
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2012-12-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
quasiperiodic solutions
slow modulations
Hamiltonian structures
Online Access:http://dx.doi.org/10.3842/SIGMA.2012.103
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spelling doaj-d20f08ca797a44498f895f2eacf434c02020-11-24T21:36:37ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592012-12-018103Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase CasesAndrei Ya. MaltsevIn 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.http://dx.doi.org/10.3842/SIGMA.2012.103quasiperiodic solutionsslow modulationsHamiltonian structures
collection DOAJ
language English
format Article
sources DOAJ
author Andrei Ya. Maltsev
spellingShingle Andrei Ya. Maltsev
Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases
Symmetry, Integrability and Geometry: Methods and Applications
quasiperiodic solutions
slow modulations
Hamiltonian structures
author_facet Andrei Ya. Maltsev
author_sort Andrei Ya. Maltsev
title Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases
title_short Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases
title_full Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases
title_fullStr Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases
title_full_unstemmed Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases
title_sort whitham's method and dubrovin-novikov bracket in single-phase and multiphase cases
publisher National Academy of Science of Ukraine
series Symmetry, Integrability and Geometry: Methods and Applications
issn 1815-0659
publishDate 2012-12-01
description 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.
topic quasiperiodic solutions
slow modulations
Hamiltonian structures
url http://dx.doi.org/10.3842/SIGMA.2012.103
work_keys_str_mv AT andreiyamaltsev whithamsmethodanddubrovinnovikovbracketinsinglephaseandmultiphasecases
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