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A method for Hamiltonian truncation: A four-wave example

A method for extracting finite-dimensional Hamiltonian systems from a class of 2+1 Hamiltonian mean field theories is presented. These theories possess noncanonical Poisson brackets, which normally resist Hamiltonian truncation, but a process of beatification by coordinate transformation near a reference state is described in order to perturbatively overcome this difficulty. Two examples of four-wave truncation of Euler's equation for scalar vortex dynamics are given and compared: one a direct non-Hamiltonian truncation of the equations of motion, the other obtained by beatifying the Poisson bracket and then truncating.

preprint2016arXivOpen access
Thiago F. ViscondiIberê L. CaldasPhilip J. Morrison
math-phmath.MPnlin.CDphysics.flu-dyn
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Thiago F. ViscondiIberê L. CaldasPhilip J. Morrison

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