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

Key Points

• Soliton solutions were successfully obtained for the discrete hirota equation under nonzero boundaries, expanding application possibilities.
• The study highlights the formulation of a riemann–hilbert problem that uses the jost solution and reflection coefficient for solution resolution.
• The analysis employed the residue theorem and laurent series to derive various soliton solutions, showcasing potential complexities.
• The findings may inspire further exploration of soliton behaviors under different conditions, indicating a broader significance in mathematical physics.