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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Zhaidary Myrzakulova & Zaruyet Zakariyeva & Anar Zhumakhanova & Kuralay Yesmakhanova, 2025. "Exact Solution of the Nonlocal PT -Symmetric (2 + 1)-Dimensional Hirota–Maxwell–Bloch System," Mathematics, MDPI, vol. 13(7), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1101-:d:1621946
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