Journal of Physics A-Mathematical and Theoretical;
APR 22 2016.
Web of Science Citations:
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. (AU)