Structure preserving noise and dissipation in the Toda lattice - Arnaudon,A (Journal of Physics A: Mathematical and Theoretical, 2018)
In this paper, we use Flaschka's change of variables of the open Toda latticeand its interpretation in term of the group structure of the LU factorisationas a coadjoint motion on a certain dual of Lie algebra to implement a structurepreserving noise and dissipation. Both preserve the structure of coadjointorbit, that is the space of symmetric tri-diagonal matrices and arise as a newtype of multiplicative noise and nonlinear dissipation of the Toda lattice. Weinvestigate some of the properties of these deformations and in particular thecontinuum limit as a stochastic Burger equation with a nonlinear viscosity.This work is meant to be exploratory, and open more questions that we cananswer with simple mathematical tools and without numerical simulations.