Lax Equation on the Uhlenbeck Manifold - Dymarskii, Ya. (Discontinuity, Nonlinearity, and Complexity, 2026)
We give an analytic and topological description of the Uhlenbeck manifold, that is a manifold of triples (a symmetric operator, an eigenvector, an eigenvalue), for the finite-dimensional symmetric matrices and the family of stationary periodic Schrodinger operators. Then, we describe an uplifting of Lax vector fields to these manifolds.