A discrete time relativistic Toda lattice

Details A discrete time relativistic Toda lattice A discrete time relativistic Toda lattice

1995-10-23

arxiv.org/abs/solv-int/9510007v1

J. Phys. A: Math. and Gen., 1996, V. 29, p. 451-465.

Nonlinear Sciences

Exactly Solvable and Integrable Systems

32 pages, LaTeX

Scientific paper

10.1088/0305-4470/29/2/022

Four integrable symplectic maps approximating two Hamiltonian flows from the relativistic Toda hierarchy are introduced. They are demostrated to belong to the same hierarchy and to examplify the general scheme for symplectic maps on groups equiped with quadratic Poisson brackets. The initial value problem for the difference equations is solved in terms of a factorization problem in a group. Interpolating Hamiltonian flows are found for all the maps.

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