Year: 2026
Type: preprint
Abstract: We construct coordinates on orthogonal conjugacy classes of traceless real symmetric matrices with arbitrary spectrum (the isospectral manifold) that diagonalize the non-periodic Toda vector field. The coordinates, defined on a neighborhood of any diagonal matrix decouple the Toda vector field into a sum of multiples of the Euler vector field in $\mathbb{R}$. The domain of each set of coordinates is dense and their union covers the isospectral manifold. The construction relies on a new matrix factorization which is of independent interest.
Source: arXiv (Cornell University)
Authors: Torres, David Martínez, Tomei, Carlos
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7202142122