Discrete time Bogoyavlensky lattices

Details Discrete time Bogoyavlensky lattices Discrete time Bogoyavlensky lattices

1995-12-20

arxiv.org/abs/solv-int/9512007v2

J. Math. Phys., 1996, V. 37, p. 3982-3996.

Nonlinear Sciences

Exactly Solvable and Integrable Systems

22 pages, LaTeX, revised version (the third lattice discretized now!)

Scientific paper

10.1063/1.531611

Discretizations of the Bogoyavlensky lattices are introduced, belonging to the same hierarchies as the continuous--time systems. The construction exemplifies the general scheme for integrable discretization of systems on Lie algebras with $r$--matrix Poisson brackets. An initial value problem for the difference equations is solved in terms of a factorization problem in a group. Interpolating Hamiltonian flow is found.

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