Weakly nonlinear dynamics in noncanonical Hamiltonian systems with applications to fluids and plasmas

A method, called beatification, is presented for rapidly extracting weakly nonlinear Hamiltonian systems that describe the dynamics near equilibria of systems possessing Hamiltonian form in terms of noncanonical Poisson brackets. The procedure applies to systems like fluids and plasmas in terms of E...

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Bibliographic Details
Published in:Annals of physics 2016-05, Vol.368 (C), p.117-147
Main Authors: Morrison, P.J., Vanneste, J.
Format: Article
Language:English
Subjects:
Brackets
Collection
Dynamical systems
Fluid dynamics
Fluids
Hamiltonian systems
Mathematical analysis
Nonlinear dynamics
Nonlinear systems
Physics
Plasmas
Poisson brackets
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Summary:A method, called beatification, is presented for rapidly extracting weakly nonlinear Hamiltonian systems that describe the dynamics near equilibria of systems possessing Hamiltonian form in terms of noncanonical Poisson brackets. The procedure applies to systems like fluids and plasmas in terms of Eulerian variables that have such noncanonical Poisson brackets, i.e., brackets with nonstandard and possibly degenerate form. A collection of examples of both finite and infinite dimensions is presented.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2016.02.003