Compatible Poisson Structures and bi-Hamiltonian Systems Related to Low-dimensional Lie Algebras
- https://doi.org/10.2991/jnmp.k.201104.001How to use a DOI?
- Compatible Poisson structures, bi-Hamiltonian system, Lie groups
In this work, we give a method to construct compatible Poisson structures on Lie groups by means of structure constants of their Lie algebras and some vector field. In this way we calculate some compatible Poisson structures on low-dimensional Lie groups. Then, using a theorem by Magri and Morosi, we obtain new integrable bi-Hamiltonian systems with two-, four- and six-dimensional symplectic real Lie groups as phase spaces.
- © 2020 The Authors. Published by Atlantis Press B.V.
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Gh. Haghighatdoost AU - S. Abdolhadi-Zangakani AU - J. Abedi-Fardad PY - 2020 DA - 2020/12 TI - Compatible Poisson Structures and bi-Hamiltonian Systems Related to Low-dimensional Lie Algebras JO - Journal of Nonlinear Mathematical Physics SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.k.201104.001 DO - https://doi.org/10.2991/jnmp.k.201104.001 ID - Haghighatdoost2020 ER -