Quasi-periodic and periodic solutions of the Toda lattice via the hyperelliptic sigma function
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Publication:2391389
DOI10.5802/aif.2772zbMath1279.14044arXiv1008.0509OpenAlexW2962772631MaRDI QIDQ2391389
Shigeki Matsutani, Emma Previato, Yuji Kodama
Publication date: 31 July 2013
Published in: Annales de l'Institut Fourier (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1008.0509
Relationships between algebraic curves and integrable systems (14H70) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Special divisors on curves (gonality, Brill-Noether theory) (14H51) Lattice dynamics; integrable lattice equations (37K60)
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Cites Work
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- A generalized Kiepert formula for \(C_{ab}\) curves
- Wannier functions for quasiperiodic finite-gap potentials
- The spectrum of difference operators and algebraic curves
- The Toda lattice, Dynkin diagrams, singularities and Abelian varieties
- Variations on a theorem of Abel
- The spectrum of Jacobi matrices
- On Cayley's explicit solution to Poncelet's porism
- Limit matrices for the Toda flow and periodic flags for loop groups
- Theta functions on Riemann surfaces
- On Dirichlet, Poncelet and Abel problems
- Jacobi inversion on strata of the Jacobian of the \(C_{rs}\) curve \(y^r = f(x)\). II
- General form of Humbert's modular equation for curves with real multiplication of \(\Delta =5\)
- Topology of the real part of the hyperelliptic Jacobian associated with the periodic Toda lattice
- Kowalevski top and genus-2 curves
- Hyperelliptic solutions of KdV and KP equations: re-evaluation of Baker's study on hyperelliptic sigma functions
- Sigma, tau and Abelian functions of algebraic curves
- Generalizations of the neumann system a curve theoretical approach-part II
- Addition formulae over the Jacobian pre-image of hyperelliptic Wirtinger varieties
- DETERMINANT EXPRESSIONS FOR HYPERELLIPTIC FUNCTIONS
- Generalizations of the neumann system a curve‐theoretical approach‐part I
- Hill and toda curves
- Generalizations of the neumann system—a curve theoretical approach part III: Order n systems
- On Some Periodic Toda Lattices
- A tower of genus two curves related to the Kowalewski top
- On the analogue of the division polynomials for hyperelliptic curves.
- Toda Equations and -Functions of Genera One and Two
- Cayley-type conditions for billiards withinkquadrics in
- Sigma Function as A Tau Function
- Abelian Functions for Trigonal Curves of Genus Three
- Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura
- Integrable systems in the realm of algebraic geometry.