3 research outputs found
On one integrable system with a cubic first integral
Recently one integrable model with a cubic first integral of motion has been
studied by Valent using some special coordinate system. We describe the
bi-Hamiltonian structures and variables of separation for this system.Comment: LaTeX with AMS fonts, 9 page
New variables of separation for particular case of the Kowalevski top
We discuss the polynomial bi-Hamiltonian structures for the Kowalevski top in
special case of zero square integral. An explicit procedure to find variables
of separation and separation relations is considered in detail.Comment: 11 pages, LaTeX with Ams font
Integrable systems on the sphere associated with genus three algebraic curves
New variables of separation for few integrable systems on the two-dimensional
sphere with higher order integrals of motion are considered in detail. We
explicitly describe canonical transformations of initial physical variables to
the variables of separation and vice versa, calculate the corresponding
quadratures and discuss some possible integrable deformations of initial
systems.Comment: 19 pages, LaTeX with AMS font