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On the canonical forms of the multi-dimensional averaged Poisson brackets
- Publication Year :
- 2015
- Publisher :
- arXiv, 2015.
-
Abstract
- We consider here special Poisson brackets given by the "averaging" of local multi-dimensional Poisson brackets in the Whitham method. For the brackets of this kind it is natural to ask about their canonical forms, which can be obtained after transformations preserving the "physical meaning" of the field variables. We show here that the averaged bracket can always be written in the canonical form after a transformation of "Hydrodynamic Type" in the case of absence of annihilators of initial bracket. However, in general case the situation is more complicated. As we show here, in more general case the averaged bracket can be transformed to a "pseudo-canonical" form under some special ("physical") requirements on the initial bracket.<br />Comment: 33 pages, Latex
- Subjects :
- Pure mathematics
Nonlinear Sciences - Exactly Solvable and Integrable Systems
010102 general mathematics
Bracket
FOS: Physical sciences
Statistical and Nonlinear Physics
Field (mathematics)
Mathematical Physics (math-ph)
Type (model theory)
01 natural sciences
Poisson bracket
Transformation (function)
Nonlinear Sciences::Exactly Solvable and Integrable Systems
Mathematics::Quantum Algebra
0103 physical sciences
Multi dimensional
Initial value problem
Canonical form
010307 mathematical physics
0101 mathematics
Exactly Solvable and Integrable Systems (nlin.SI)
Mathematics::Symplectic Geometry
Mathematical Physics
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....361808e567322257bea2c5b77ef47916
- Full Text :
- https://doi.org/10.48550/arxiv.1502.04468