Darboux transformations and solutions of nonlocal Hirota and Maxwell–Bloch equations. Issue 1 (16th March 2021)

• Record Type: Journal Article
• Authors: An, Ling; Li, Chuanzhong; Zhang, Lixiang
• Is Part Of: Studies in applied mathematics. Volume 147:Issue 1(2021)
• Page Start: 60
• Page End: 83
• Publication Date: 2021-03-16
• Subjects: Darboux transformation -- explicit solution -- nonlocal Hirota and Maxwell–Bloch system; Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/sapm.12378
• Languages: English
• ISSNs: 0022-2526

Abstract

Abstract: In this paper, based on the Hirota and Maxwell–Bloch (H‐MB) system and its application in the theory of the femtosecond pulse propagation through an erbium doped fiber, we define two kinds of nonlocal Hirota and Maxwell–Bloch (NH‐MB) systems, namely, P T ‐symmetric NH‐MB system and reverse space‐time NH‐MB system. Then, we construct the Darboux transformations of these NH‐MB systems. Meanwhile, we derive the explicit solutions by the Darboux transformations.