Toda晶格中的保结构噪声和耗散
Structure preserving noise and dissipation in the Toda lattice
摘要：
在本文中，我们使用Flaschka的变量的开放Toda格和它的解释的LU分解作为一个coadjoint运动在一定的对偶李代数实现的结构保持噪声和耗散的组结构。两者都保持了共伴轨道的结构，即对称三对角矩阵的空间，并作为Toda晶格的新型乘性噪声和非线性耗散而出现。我们调查这些变形的一些性质，特别是连续极限作为一个随机Burger方程的非线性粘性。这项工作是探索性的，并提出了更多的问题，我们可以用简单的数学工具来回答，而不需要数值模拟。
英文摘要：
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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