Backlund transformations on coadjoint orbits of the loop algebra gl(n)
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hdl:2117/1200
Tipus de documentArticle
Data publicació2003
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Abstract
There is a wide class of integrable Hamiltonian systems on finite-dimensional coadjoint
orbits of the loop algebra ˜ gl(r) which are represented by r × r Lax equations with a
rational spectral parameter.A reduced complex phase space is foliated with open
subsets of Jacobians of regularized spectral curves.Under some generic restrictions
on the structure of the Lax matrix, we propose an algebraic geometrical scheme of a
discretization of such systems that preserve their first integrals and is represented as
translations on the Jacobians.A generic discretizing map is given implicitly in the form
of an intertwining relation (a discrete Lax pair) with an extra parameter governing
the translation.Some special cases when the map is explicit are also considered.As
an example, we consider a modified discrete version of the classical Neumann system
described by a 2 × 2 discrete Lax pair and provide its theta-functional solution.
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