A discrete time peakons lattice

Abstract

A discretization of the peakons lattice is introduced, belonging to the same hierarchy as the continuous--time system. The construction examplifies 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. A variational (Lagrangian) formulation is also given.

14 pages, LaTeX

References in corpus (5)

• An integrable shallow water equation with peaked solitons
• Integrable Time-Discretisation of the Ruijsenaars-Schneider Model
• A discrete time relativistic Toda lattice
• A time-discretized version of the Calogero-Moser model
• Dynamical R-Matrices for Integrable Maps

Cited by in corpus (6)

• The Camassa-Holm Equation: A Loop Group Approach
• Wave Solutions of Evolution Equations and Hamiltonian Flows on Nonlinear Subvarieties of Generalized Jacobians
• A note on the integrable discretization of the nonlinear Schrödinger equation
• Smooth and Peaked Solitons of the CH equation
• On an integrable discretization of the modified Korteweg-de Vries equation
• Integrable discretizations of the spin Ruijsenaars-Schneider models