Nonlinear Dynamics

, Volume 89, Issue 3, pp 1637–1649 | Cite as

Systematic generation of higher-order solitons and breathers of the Hirota equation on different backgrounds

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

Abstract

We investigate the systematic generation of higher-order solitons and breathers of the Hirota equation on different backgrounds. The Darboux transformation is used to construct proper initial conditions for dynamical generation of high-intensity solitons and breathers of different orders on a uniform background. We provide expressions for the Lax pair generating functions and the procedure for calculating higher-order solutions when Jacobi elliptic functions are the background seed solutions of the Hirota equation. We confirm that the peak height of each soliton or breather in the nonlinear Darboux superposition adds linearly, to form the intensity maximum of the final solution.

Keywords

Hirota equation Darboux transformation Higher-order solitons Breathers and rogue waves 

Notes

Acknowledgements

This research is supported by the Qatar National Research Fund (Projects NPRP 6-021-1-005 and NPRP 8-028-1-001), a member of the Qatar Foundation. S.N.N. acknowledges support from Grants III45016 and OI171038 of the Serbian Ministry of Education, Science and Technological Development. N.B.A. acknowledges support from Grant OI171006 of the Serbian Ministry of Education, Science and Technological Development. M.R.B. acknowledges support by the Al-Sraiya Holding Group.

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

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

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