New degeneration of Fay's identity and its application to integrable systems

TL;DR

This paper introduces a new degenerated form of Fay's identity and applies it to derive novel algebro-geometric solutions for integrable systems like the multi-component nonlinear Schrödinger equation and the Davey-Stewartson equations.

Contribution

It presents a new degenerated Fay's identity and demonstrates its use in constructing and deriving solutions for key integrable systems.

Findings

New degenerated Fay's identity proved

Constructed new solutions for multi-component nonlinear Schrödinger equation

Derived known solutions for Davey-Stewartson equations

Abstract

In this paper we prove a new degenerated version of Fay's trisecant identity. The new identity is applied to construct new algebro-geometric solutions of the multi-component nonlinear Schr\"odinger equation. This approach also provides an independent derivation of known algebro-geometric solutions to the Davey-Stewartson equations.