Tau functions and KP solutions on families of algebraic curves

2022/08/15 by Takashi Ichikawa, Ichikawa, Takashi
Physics and Astronomy · Computer Science · Mathematics · #Nonlinear Waves and Solitons #Polynomial and algebraic computation #Commutative Algebra and Its Applications

paper · pdf · doi:10.48550/arxiv.2208.07013

Abstract

Using abelian differentials and periods of the universal Mumford curve, we study the universal expression and asymptotic behavior of tau functions defined for stably degenerating families of algebraic curves with additional data. Furthermore, we apply this study to constructing solutions to the KP hierarchy which are expressed by nonarchimedean theta functions and by mixtures of quasi-periodic solutions with solitons containing real solutions defined on families of M-curves.

Related

• On Algebraic Theta Divisors and Rational Solutions of the KP Equation
• Super Curves, their Jacobians, and super KP equations
• Soliton Solutions of Kortweg-de Vries Equations and Hyperelliptic Sigma Functions
• The universal Mumford curve, and its abelian differentials and periods in arithmetic formal geometry
• Families of KP solutions associated with tropical curves having nontrivial weights