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arXiv · 1804.03480

Structure preserving noise and dissipation in the Toda lattice

Alexis Arnaudon
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Abstract

In this paper, we use Flaschka's change of variables of the open Toda lattice and its interpretation in term of the group structure of the LU factorisation as a coadjoint motion on a certain dual of Lie algebra to implement a structure preserving noise and dissipation. Both preserve the structure of coadjoint orbit, that is the space of symmetric tri-diagonal matrices and arise as a new type of multiplicative noise and nonlinear dissipation of the Toda lattice. We investigate some of the properties of these deformations and in particular the continuum limit as a stochastic Burger equation with a nonlinear viscosity. This work is meant to be exploratory, and open more questions that we can answer with simple mathematical tools and without numerical simulations.

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Alexis Arnaudon. 2018-04-10. Structure preserving noise and dissipation in the Toda lattice. https://doi.org/10.1088/1751-8121/aabcec

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