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Lax pair, Darboux transformation, vector rational and semi-rational rogue waves for the three-component coupled Hirota equations in an optical fiber

  • Zhong Du
  • Bo TianEmail author
  • Han-Peng Chai
  • Xue-Hui Zhao
Regular Article
  • 3 Downloads

Abstract.

The optical fiber communication system is one of the supporting systems of the modern internet age. In this paper, we study the three-component coupled Hirota equations, which govern the simultaneous propagation of three fields in the normal dispersion regime of an optical fiber. We derive a Lax pair and construct the corresponding Darboux transformation. Via the Darboux transformation, rogue wave solutions with the corresponding characteristic polynomial admiting a quadruple root and two/one double roots are obtained. Via such solutions, we depict the first-order vector rational rogue wave with the two components containing the four-petaled rogue wave, and the other component containing one eye-shaped rogue wave; increasing the value of the real parameter which denotes the integrable perturbation, we observe that the range of the first-order vector rational rogue wave along an axis increases; we display the first-order vector rational rogue waves with each component containing two/three merged and separated rogue waves. The second-order rogue waves are graphically displayed, with each component containing five, seven or nine rogue waves, which form the pentagon, triangle, clawlike, hexagon, arrow, line or trapezoid structures. The first- and second-order vector rational/semi-rational rogue waves are graphically exhibited. Two types of the vector semi-rational rogue waves are presented: the one with each component containing the rogue waves and line breathers, and the other with each component containing the rogue waves and Y-shaped breathers.

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Copyright information

© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Zhong Du
    • 1
  • Bo Tian
    • 1
    Email author
  • Han-Peng Chai
    • 1
  • Xue-Hui Zhao
    • 1
  1. 1.State Key Laboratory of Information Photonics and Optical Communications, and School of ScienceBeijing University of Posts and TelecommunicationsBeijingChina

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