The Riemann–Hilbert Approach for the Discrete Hirota Equations in a Nonzero Background

The primary objective of this article is to obtain soliton solutions for the discrete Hirota equation under nonzero boundary conditions, utilizing the Riemann–Hilbert approach. A suitable Riemann–Hilbert problem was formulated employing the Jost solution and the reflection coefficient. The potential was subsequently resolved through the application of the residue theorem and the Laurent series. The study presents soliton solutions associated with simple poles as well as higher order poles of the discrete Hirota equation and explores specific soliton solutions.