A Bi-Hamiltonian Formulation for Triangular Systems by Perturbations
Exactly Solvable and Integrable Systems
2009-11-07 v1
Abstract
A bi-Hamiltonian formulation is proposed for triangular systems resulted by perturbations around solutions, from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed, provided that one operator of the Hamiltonian pair is invertible. Through our formulation, four examples of triangular systems are exhibited, which also show that bi-Hamiltonian systems in both lower dimensions and higher dimensions are many and varied. Two of four examples give local 2+1 dimensional bi-Hamiltonian systems and illustrate that multi-scale perturbations can lead to higher-dimensional bi-Hamiltonian systems.
Cite
@article{arxiv.nlin/0112009,
title = {A Bi-Hamiltonian Formulation for Triangular Systems by Perturbations},
author = {Wen-Xiu Ma},
journal= {arXiv preprint arXiv:nlin/0112009},
year = {2009}
}
Comments
16 pages, to appear in J. Math. Phys