Integrable discretizations for lattice systems: local equations of motion and their Hamiltonian properties

Details Integrable discretizations for lattice systems: local equations of motion and their Hamiltonian properties Integrable discretizations for lattice systems: local equations of motion and their Hamiltonian properties

1997-09-18

arxiv.org/abs/solv-int/9709005v4

Rev. Math. Phys., 1999, V.11, p. 727-822.

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTeX, 89pp; section on modified Volterra added

Scientific paper

We develop the approach to the problem of integrable discretization based on the notion of $r$--matrix hierarchies. One of its basic features is the coincidence of Lax matrices of discretized systems with the Lax matrices of the underlying continuous time systems. A common feature of the discretizations obtained in this approach is non--locality. We demonstrate how to overcome this drawback. Namely, we introduce the notion of localizing changes of variables and construct such changes of variables for a large number of examples, including the Toda and the relativistic Toda lattices, the Volterra lattice and its integrable perturbation, the second flows of the Toda and of the Volterra hierarchies, the modified Volterra lattice, the Belov-Chaltikian lattice, the Bogoyavlensky lattices, the Bruschi-Ragnisco lattice. We also introduce a novel class of constrained lattice KP systems, discretize all of them, and find the corresponding localizing change of variables. Pulling back the differential equations of motion under the localizing changes of variables, we find also (sometimes novel) integrable one-parameter perturbations of integrable lattice systems. Poisson properties of the localizing changes of variables are also studied: they produce interesting one-parameter deformations of the known Poisson algebras.

Affiliated with

Also associated with

No associations

Rating

Integrable discretizations for lattice systems: local equations of motion and their Hamiltonian properties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Integrable discretizations for lattice systems: local equations of motion and their Hamiltonian properties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Integrable discretizations for lattice systems: local equations of motion and their Hamiltonian properties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-691905