Breathers, solitons and rogue waves of the quintic nonlinear Schrödinger equation on various backgrounds

  • Stanko N. NikolićEmail author
  • Omar A. Ashour
  • Najdan B. Aleksić
  • Milivoj R. Belić
  • Siu A. Chin
Original Paper


We investigate the generation of breathers, solitons, and rogue waves of the quintic nonlinear Schrödinger equation (QNLSE) on uniform and elliptical backgrounds. The QNLSE is the general nonlinear Schrödinger equation that includes all terms up to the fifth-order dispersion. We use Darboux transformation to construct initial conditions for the dynamical generation of localized high-intensity optical waves. The condition for the breather-to-soliton conversion is provided with the analysis of soliton intensity profiles. We discover a new class of higher-order solutions in which Jacobi elliptic functions are set as background seed solutions of the QNLSE. We also introduce a method for generating a new class of rogue waves—the periodic rogue waves—based on the matching of the periodicity of higher-order breathers with the periodicity of the background dnoidal wave.


Quintic nonlinear Schrödinger equation Darboux transformation Rogue waves 



This research is supported by the Qatar National Research Fund (Project NPRP 8-028-1-001). S.N.N. acknowledges support from Grants III 45016 and OI 171038 of the Serbian Ministry of Education, Science and Technological Development. N.B.A. acknowledges support from Grant OI 171006 of the Serbian Ministry of Education, Science and Technological Development. O.A.A. is supported by the Berkeley Graduate Fellowship and the Anselmo J. Macchi Graduate Fellowship. M.R.B. acknowledges support by the Al-Sraiya Holding Group.

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

  • Stanko N. Nikolić
    • 1
    • 2
    Email author
  • Omar A. Ashour
    • 3
    • 4
  • Najdan B. Aleksić
    • 1
    • 2
  • Milivoj R. Belić
    • 2
  • Siu A. Chin
    • 3
  1. 1.Institute of Physics BelgradeUniversity of BelgradeBelgradeSerbia
  2. 2.Science programTexas A&M University at QatarDohaQatar
  3. 3.Department of Physics and AstronomyTexas A&M UniversityCollege StationUSA
  4. 4.Department of PhysicsUniversity of CaliforniaBerkeleyUSA

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