Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2002-05-15
Nonlinear Sciences
Exactly Solvable and Integrable Systems
LaTeX, 11pages
Scientific paper
10.1063/1.1501446
For finite dimensional Hamiltonian systems derived from 1+1 dimensional integrable systems, if they have Lax representations, then the Lax operator creates a set of conserved integrals. When these conserved integrals are in involution, it is believed quite popularly that there will be enough functionally independent ones among them to guarantee the Liouville integrability of the Hamiltonian systems, at least for those derived from physical problems. In this paper, we give a counterexample based on the U(2) principal chiral field. It is proved that the finite dimensional Hamiltonian systems derived from the U(2) principal chiral field are Liouville integrable. Moreover, their Lax operator gives a set of involutive conserved integrals, but they are not enough to guarantee the integrability of the Hamiltonian systems.
No associations
LandOfFree
Liouville integrability of the finite dimensional Hamiltonian systems derived from principal chiral field does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Liouville integrability of the finite dimensional Hamiltonian systems derived from principal chiral field, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Liouville integrability of the finite dimensional Hamiltonian systems derived from principal chiral field will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-239756