Dynamics of solitons in the fourth-order nonlocal nonlinear Schrödinger equation

  • T. A. GadzhimuradovEmail author
  • A. M. Agalarov
  • R. Radha
  • B. Tamil Arasan
Original paper


We consider the fourth-order nonlocal nonlinear Schrödinger equation and generate the Lax pair. We then employ Darboux transformation to generate dark and antidark soliton solutions. The highlight of the results is that one ends up generating a two-soliton solution characterized by one spectral parameter alone, a property which has never been witnessed so far.


Nonlocal nonlinear equations Lax pair Darboux transformation \(\mathcal {P}\mathcal {T}\) symmetry Soliton 



Authors thank Dr. V. G. Marikhin for his remarks and discussions. This work was supported, in part, by Grant No. 14-11-0039. R. Radha wishes to acknowledge financial assistance received from Council of Scientific and Industrial Research (No. 03(1456)/19/EMR-II Dated: 05/08/2019), Government of India.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • T. A. Gadzhimuradov
    • 1
    Email author
  • A. M. Agalarov
    • 1
  • R. Radha
    • 2
  • B. Tamil Arasan
    • 3
  1. 1.Department of Theoretical Physics, Institute of Physics Dagestan Scientific CentreRussian Academy of ScienceMakhachkalaRussia
  2. 2.Centre for Nonlinear Science (CeNSc), Post-Graduate and Research Department of PhysicsGovernment College for Women (Autonomous)KumbakonamIndia
  3. 3.Department of Physics, Presidency College (Autonomous)University Of MadrasChennaiIndia

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