English

A method for Hamiltonian truncation: A four-wave example

Fluid Dynamics 2016-01-13 v2 Mathematical Physics math.MP Chaotic Dynamics

Abstract

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.

Keywords

Cite

@article{arxiv.1509.09247,
  title  = {A method for Hamiltonian truncation: A four-wave example},
  author = {Thiago F. Viscondi and Iberê L. Caldas and Philip J. Morrison},
  journal= {arXiv preprint arXiv:1509.09247},
  year   = {2016}
}

Comments

27 pages, 1 figure; references added

R2 v1 2026-06-22T11:09:23.586Z