Soliton Fay identities. II. Bright soliton case

TL;DR

This paper introduces generalized bilinear matrix identities that facilitate the construction of bright soliton solutions, demonstrated through deriving N-bright solitons for the Ablowitz-Ladik hierarchy.

Contribution

It presents new bilinear matrix identities that extend existing methods for constructing bright soliton solutions in integrable models.

Findings

Derived a set of generalized bilinear matrix identities.

Applied identities to obtain N-bright soliton solutions for Ablowitz-Ladik hierarchy.

Simplified the derivation process for bright soliton solutions.

Abstract

We present a set of bilinear matrix identities that generalize the ones that have been used to construct the bright soliton solutions for various models. As an example of an application of these identities, we present a simple derivation of the N-bright soliton solutions for the Ablowitz-Ladik hierarchy.