2024/01/16 by Bertrand Eynard, Eynard, Bertrand, Soufiane Oukassi +1
Mathematics · Physics and Astronomy · #14H42 #14H70 #37K10 #Algebraic structures and combinatorial models #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2401.08317
openalex publication_date 2024/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This is a review of the relationship between Fay identities and Hirota equations in integrable systems, reformulated in a geometric language compatible with recent Topological Recursion formalism. We write Hirota equations as trans-series, and Fay identities as spinor functional relations. We also recall several constructions of how some solutions to Fay/Hirota equations can be built from Riemann surface geometry.