The nonlocal nonlinear Schrödinger and Maxwell – Bloch equation

  • Sh. R. Myrzakul Faculty of Physics and Technology, al-Farabi Kazakh National University, Almaty, Kazakhstan
  • E. Gudekli Department of Physics, Istanbul University, Istanbul, Turkey
  • A. M. Syzdyk Faculty of physics and technical sciences, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
  • K. R. Yesmakhanova Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan

Abstract

In this paper, the nonlocal nonlinear Schrцdinger and Maxwell – Bloch equations are is introduced. A particular case of this system, namely the Schrцdinger equation, is integrable by the inverse scattering method as shown in the work of M. Ablowitz and Z. Musslimani. Following their idea, we prove the integrability of the nonlocal nonlinear Schrцdinger and Maxwell – Bloch equation using its Lax pairs. Also the Darboux transformations are constructed, and soliton solutions are obtained from different "seed" solutions using them. One–fold, two–fold and N–fold determinant representations are obtained by this transformation. Moreover, soliton and solitons–like solutions, such as dynamic and topological soliton, periodic, domain walls, kink, lamp, bright and dark solitons, bright and dark rogue waves, bright and dark positons, etc., of this equation are built. In future papers, we will investigate the conservation laws of the nonlocal nonlinear Schrцdinger and Maxwell – Bloch equation using the Lax pair.

 
 


 

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АнглийскийИспанскийИтальянскийКазахскийКитайский ТрадКитайский УпрКорейскийРусскийТурецкийФранцузский
 
АнглийскийИспанскийИтальянскийКазахскийКитайский ТрадКитайский УпрКорейскийРусскийТурецкийФранцузский
 
 
 
 
 


 
 
 
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Published
Dec 25, 2017
How to Cite
MYRZAKUL, Sh. R. et al. The nonlocal nonlinear Schrödinger and Maxwell – Bloch equation. International Journal of Mathematics and Physics, [S.l.], v. 8, n. 2, p. 4-12, dec. 2017. ISSN 2409-5508. Available at: <http://ijmph.kaznu.kz/index.php/kaznu/article/view/224>. Date accessed: 11 dec. 2018. doi: https://doi.org/10.26577/ijmph.v8i2.224.