Higher order degenerations of Fay's identities and applications to integrable equations

TL;DR

This paper develops higher order degenerated Fay identities and demonstrates their application in deriving solutions to Schwarzian KP equations, advancing the understanding of integrable systems.

Contribution

It introduces higher order degenerated Fay identities and applies them to generate solutions for Schwarzian KP equations, a novel approach in integrable systems.

Findings

Derived higher order degenerated Fay identities.

Connected Fay identities to Schwarzian KP solutions.

Provided new methods for solving integrable equations.

Abstract

Higher order degenerated versions of Fay's trisecant identity are presented. It is shown that these lead to solutions for Schwarzian Kadomtsev-Petviashvili equations.