Finite-gap solutions of the Fuchsian equations

DOI10.1007/s11005-006-0070-xzbMath1136.34065arXivmath/0310465OpenAlexW2088185846WikidataQ57936777 ScholiaQ57936777MaRDI QIDQ2457229

Aleksandr Olegovich Smirnov

Publication date: 30 October 2007

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0310465

zbMATH Keywords

Schrödinger operatorsfinite-gap solutionsHeun equationFuchsian equations

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Relationships between algebraic curves and integrable systems (14H70)

Related Items

The Hermite-Krichever ansatz for Fuchsian equations with applications to the sixth Painlevé equation and to finite-gap potentials ⋮ On the spectral curve for functional-difference Schrödinger equation ⋮ On Darboux-Treibich-Verdier potentials ⋮ A Riemann-Hilbert approach to the Heun equation ⋮ Elliptic solitons, Fuchsian equations, and algorithms ⋮ The 192 solutions of the Heun equation

Cites Work

• Verdier elliptic solitons and the Weierstrass theory of reduction
• Exceptional coverings and sums of 4 triangular numbers
• Reduction of theta functions and elliptic finite-gap potentials
• Finite-gap elliptic solutions of the KdV equation
• Picard potential and Hill's equation on a torus
• On Picard potentials
• Au-delà des potentiels et revêtements tangentiels hyperelliptiques exceptionnels
• The Heun Equation and the Calogero-Moser-Sutherland System III: The Finite-Gap Property and the Monodromy
• An explicit characterization of Calogero–Moser systems
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