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

Abstract

A method, called beatification, is presented for rapidly extracting weakly nonlinear Hamiltonian systems that describe the dynamics near equilibria for 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.

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Cited by in corpus (7)

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• Derivation of the Hall and Extended Magnetohydrodynamics Brackets
• A General Metriplectic Framework with Application to Dissipative Extended Magnetohydrodynamics
• Lifting of the Vlasov-Maxwell Bracket by Lie-transform Method
• Beatification: Flattening the Poisson Bracket for Two-Dimensional Fluid and Plasma Theories
• Towards a classification of bifurcations in Vlasov equations
• Hamiltonian Nature of Monopole Dynamics