Combinatorics of multisecant Fay identities

2020/10/29 by Vekslerchik, V. E.
#05A19 #14K25 #35Q51 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2010.15473

Abstract

We derive a set of identities for the theta functions on compact Riemann surfaces which generalize the famous trisecant Fay identity. Using these identities we obtain quasiperiodic solutions for a multidimensional generalization of the Hirota bilinear difference equation and for a multidimensional Toda-type system.

Related

• Finite-genus solutions for the Hirota's bilinear difference equation
• Hirota, Fay and Geometry
• Quasi-periodic solutions to hierarchies of nonlinear integrable equations and bilinear relations
• Quasi-periodic and periodic solutions of the Toda lattice via the hyperelliptic sigma function
• Quasi-periodic solutions of the universal hierarchy