Explicit solutions of nonlocal reverse-time Hirota-Maxwell-Bloch system

Zh. Myrzakulova, Z. Zakariyeva, K. Suleimenov, U. Uralbekova and K. Yesmakhanova

In this paper, we investigate the nonlocal reverse-time Hirota-Maxwell-Bloch system, focusing on its soliton solutions using the Darboux transformation method. By deriving the Darboux transformation for this system, we obtained explicit expressions for the new potentials q′, p′, and η′ in both the defocusing (κ = 1) and focusing (κ = −1) cases. Our analysis reveals significant differences in soliton behavior depending on the value of κ, with the defocusing case producing wide, smooth solitons and the focusing case yielding narrow, highly localized solitons. These results provide a deeper understanding of soliton dynamics in nonlocal integrable systems and lay the groundwork for future studies on the influence of nonlocality in integrable models.

Reference to the article: Myrzakulova, Z., Zakariyeva, Z., Suleimenov, K., Uralbekova, U., & Yesmakhanova, K. (2024). Explicit solutions of nonlocal reverse-time Hirota-Maxwell-Bloch system. AIMS Math, 9, 35004-35015. https://www.aimspress.com/article/doi/10.3934/math.20241666