Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2010-11-14
Nonlinear Sciences
Exactly Solvable and Integrable Systems
37 pages
Scientific paper
We propose a new construction of two-dimensional natural bi-Hamiltonian systems associated with a very simple Lie algebra. The presented construction allows us to distinguish three families of super-integrable monomial potentials for which one additional first integral is quadratic, and the second one can be of arbitrarily high degree with respect to the momenta. Many integrable systems with additional integrals of degree greater than two in momenta are given. Moreover, an example of a super-integrable system with first integrals of degree two, four and six in the momenta is found.
Przybylska Maria
Tsiganov Andrey V.
~Maciejewski Andrzej J.
No associations
LandOfFree
On algebraic construction of certain integrable and super-integrable systems 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 On algebraic construction of certain integrable and super-integrable systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On algebraic construction of certain integrable and super-integrable systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-297502