An inhomogeneous Lax representation for the Hirota equation

TL;DR

This paper introduces an inhomogeneous Lax representation for the Hirota equation, expanding the understanding of integrable models without U(1) symmetry and deriving new Hirota-like equations.

Contribution

It presents a novel inhomogeneous Lax representation for the Hirota equation, revealing a new family of compatible Hirota-like equations in integrable systems.

Findings

Established an inhomogeneous Lax representation for the Hirota equation

Derived a new family of Hirota-like equations

Extended the framework for quantum integrable models without U(1) symmetry

Abstract

Motivated by recent work on quantum integrable models without U(1) symmetry, we show that the sl(2) Hirota equation admits a Lax representation with inhomogeneous terms. The compatibility of the auxiliary linear problem leads to a new consistent family of Hirota-like equations.