Eur. Phys. J. Plus (2019) 134: 213
https://doi.org/10.1140/epjp/i2019-12515-4

Regular Article

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

State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, 100876, Beijing, China

^* e-mail: tian_bupt@163.com

Received: 20 August 2018
Accepted: 15 January 2019
Published online: 22 May 2019

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.