Weakly nonlinear dynamics in noncanonical Hamiltonian systems with applications to fluids and plasmas |
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Authors: | PJ Morrison J Vanneste |
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Institution: | 1. Department of Physics and Institute for Fusion Studies, University of Texas, Austin, USA;2. School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, UK |
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Abstract: | 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. |
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Keywords: | Fluids Plasmas Hamiltonian systems Poisson brackets |
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