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Z. Naturforsch. 69a, 521 – 531 (2014)
doi:10.5560/ZNA.2014-0045
Multi-Soliton and Rogue-Wave Solutions of the Higher-Order Hirota System for an Erbium-Doped Nonlinear Fiber
Da-Wei Zuo1,2, Yi-Tian Gao1, Yu-Hao Sun1, Yu-Jie Feng1, and Long Xue1
1 State Key Laboratory of Software Development Environment and Ministry-of-Education Key Laboratory of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
2 Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
Received March 17, 2014 / revised May 11, 2014 / published online August 13, 2014
Reprint requests to: Y.-T. G.; E-mail: gaoyt163@163.com
The nonlinear Schrödinger (NLS) equation appears in fluid mechanics, plasma physics, etc., while the Hirota equation, a higher-order NLS equation, has been introduced. In this paper, a higher-order Hirota system is investigated, which describes the wave propagation in an erbium-doped nonlinear fiber with higher-order dispersion. By virtue of the Darboux transformation and generalized Darboux transformation, multi-soliton solutions and higher-order rogue-wave solutions are derived, beyond the published first-order consideration. Wave propagation and interaction are analyzed: (i) Bell-shape solitons, bright- and dark-rogue waves are found; (ii) the two-soliton interaction is elastic, i. e., the amplitude and velocity of each soliton remain unchanged after the interaction; (iii) the coefficient in the system affects the direction of the soliton propagation, patterns of the soliton interaction, distance, and direction of the first-order rogue-wave propagation, as well as the range and direction of the second-order rogue-wave interaction.
Key words: Optical Fiber; Higher-Order Hirota System; Darboux Transformation; Multi-Soliton Solutions; Rogue-Wave Solutions.
PACS numbers: 47.35.Fg; 05.45.Yv; 02.30.Jr
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