https://doi.org/10.1140/epjp/s13360-022-03286-2
Regular Article
The generalized Darboux transformation and higher-order rogue waves for a coupled nonlinear Schrödinger system with the four-wave mixing terms in a birefringent fiber
State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, 100876, Beijing, China
Received:
28
June
2022
Accepted:
14
September
2022
Published online:
3
November
2022
Optical communication systems play a role in the modern long-distance communication networks due to their characteristics of the low-loss transmission over the long distances and ultra-high capacities. We investigate a coupled nonlinear Schrödinger system with the four-wave mixing terms which describes the optical nonlinear waves in a birefringent fiber. We construct a generalized Darboux transformation which is different from the published ones, with which we obtain the higher-order rogue-wave solutions. Based on those solutions, 1. five structures of the second-order rogue-wave pairs which contain four or six rogue waves are shown, i.e., the line, rhombus, triangle, quadrilateral and pentagon structures; 2. we present the pentagon structure of the third-order rogue wave, which is composed of five four-petaled rogue waves, and then we find one four-petaled rogue wave in the internal region of the pentagon structure; 3. six four-petaled rogue waves form the triangle structure of the third-order rogue wave; 4. the third-order rogue wave consisting of three four-petaled rogue waves and one eye-shaped rogue wave is depicted; and 5. the fourth-order rogue wave consisting of three four-petaled rogue waves and three eye-shaped rogue waves is shown.
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