Schlesinger system, Einstein equations and hyperelliptic curves
D.Korotkin, V.Matveev
TL;DR
This paper reviews recent advances in algebro-geometric methods for solving integrable systems, focusing on theta-functional solutions of the Schlesinger system, Ernst equation, and Einstein equations.
Contribution
It highlights new developments in the algebro-geometric integration techniques applied to important physical and mathematical systems.
Findings
Theta-functional solutions for Schlesinger system
Explicit solutions for Ernst equation
Applications to self-dual Einstein equations
Abstract
We review recent developments in the method of algebro-geometric integration of integrable systems related to deformations of algebraic curves. In particular, we discuss the theta-functional solutions of Schlesinger system, Ernst equation and self-dual SU(2)-invariant Einstein equations.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Algebra and Geometry · Algebraic structures and combinatorial models