Exact Solution of the Nonlocal PT-Symmetric (2 + 1)-Dimensional Hirota–Maxwell–Bloch System
Myrzakulova Z. Zakariyeva Z. Zhumakhanova A. Yesmakhanova K.
April 2025Multidisciplinary Digital Publishing Institute (MDPI)
Mathematics
2025#13Issue 7
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.
Darboux transformation , Hirota–Maxwell–Bloch equation , nonlocal system , PT-symmetry
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Faculty of Mechanics and Mathematics, L.N. Gumilyov, Eurasian National University, 13 Kazhymukan, Astana, 010008, Kazakhstan
Faculty of Physics and Mathematics, M. Utemisov West Kazakhstan University, 162 Nazarbayev, Oral, 090000, Kazakhstan
Faculty of Mechanics and Mathematics
Faculty of Physics and Mathematics
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