Finite-gap solutions of the Fuchsian equation
Alexander O. Smirnov
TL;DR
This paper introduces a new class of Fuchsian equations with solutions linked to hyperelliptic curves, providing methods to compute their algebraic genus and branching points, supported by numerous examples.
Contribution
It presents a novel class of Fuchsian equations with algebraic geometric solutions related to hyperelliptic curves, including methods for calculating their genus and branch points.
Findings
New class of Fuchsian equations with hyperelliptic curve solutions
Methods for calculating algebraic genus and branching points
Numerous illustrative examples
Abstract
We find a new class of the Fuchsian equations, which have an algebraic geometric solutions with the parameter belonging to a hyperelliptic curve. Methods of calculating the algebraic genus of the curve, and its branching points, are suggested. Numerous examples are given.
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 Differential Equations and Dynamical Systems · Geometry and complex manifolds