Exact Solution of the Nonlocal PT -Symmetric (2 + 1)-Dimensional Hirota–Maxwell–Bloch System

Zhaidary Myrzakulova (), Zaruyet Zakariyeva, Anar Zhumakhanova and Kuralay Yesmakhanova ()
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Zhaidary Myrzakulova: Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 13 Kazhymukan, Astana 010008, Kazakhstan
Zaruyet Zakariyeva: Faculty of Physics and Mathematics, M. Utemisov West Kazakhstan University, 162 Nazarbayev, Oral 090000, Kazakhstan
Anar Zhumakhanova: Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 13 Kazhymukan, Astana 010008, Kazakhstan
Kuralay Yesmakhanova: Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 13 Kazhymukan, Astana 010008, Kazakhstan

Mathematics, 2025, vol. 13, issue 7, 1-13

Abstract: This paper investigates the (2 + 1)-dimensional nonlocal Hirota–Maxwell–Bloch (NH-MB) system under various types of nonlocality. The mathematical consistency of possible nonlocal structures is analyzed, and three types that lead to a well-posed system are identified. The integrability of the system is established through its Lax pair representation, and a Darboux transformation is constructed. Exact soliton solutions are obtained for both the defocusing and focusing cases. The results obtained may find applications in nonlinear optics, quantum theory, and the theory of integrable systems.

Keywords: nonlocal system; PT -symmetry; Hirota–Maxwell–Bloch equation; Darboux transformation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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