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Backlund transformations on coadjoint orbits of the loop algebra gl(n)
Fedorov, Yuri
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
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.
Difference equations
Hamiltonian systems
Loop Algebra
Equacions en diferències
Hamilton, Sistemes de
Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
Classificació AMS::39 Difference and functional equations::39A Difference equations
Attribution-NonCommercial-NoDerivs 2.5 Spain

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