Soliton Fay identities. I. Dark soliton case

TL;DR

This paper derives bilinear identities for determinants used in constructing dark soliton solutions and demonstrates their application across various multidimensional nonlinear models.

Contribution

It introduces new bilinear identities for determinants related to dark soliton solutions and applies them to multiple complex multidimensional systems.

Findings

Derived bilinear identities for dark soliton determinants

Applied identities to multidimensional quadrilateral lattices

Provided explicit dark soliton solutions for several models

Abstract

We derive a set of bilinear identities for the determinants of the matrices that have been used to construct the dark soliton solutions for various models. To give examples of the application of the obtained identities we present soliton solutions for the equations describing multidimensional quadrilateral lattices, Darboux equations and multidimensional multicomponent systems of the nonlinear Schrodinger type.