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Many classical integrable systems admit a bi-Hamiltonian formulation, which means
that the equations of motion can be encoded using two different Poisson brackets and
corresponding Hamiltonians. After recalling this notion, we present a bi-Hamiltonian
structure for the finite dimensional dynamical systems derived by Braden and Hone in
1996 from the solitons of affine Toda field theory. These evolution equations have been
related to the so called spin Ruijsenaars-Schneider model as well as to the hyperbolic spin Sutherland model that arises by reduction of free geodesic motion on a symmetric space.The integrable models just mentioned describe interacting point `particles'
moving along a line and include also `spin' degrees of freedom akin to time dependent
coupling parameters. The second half of the lecture is devoted to analogous models of
particles moving on a circle. In this case a bi-Hamiltonian structure will be derived via
reducing a bi-Hamiltonian structure associated with free geodesic motion on the unitary
group U(n). The talk is based on the papers arXiv:1901.03558 and arXiv:1908.02467.
Az előadás felvétele a következő linkről érhető el:
https://mydrive.kfki.hu/f/cd5ca02477664df48d8c/