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Asymptotic analysis on bright solitons and breather solutions of a generalized higher-order nonlinear Schrödinger equation in an optical fiber or a planar waveguide |
| Xin Zhao(赵鑫)1,†, Zhong Du(杜仲)2, Li-Jian Zhou(周立俭)1, Rong-Xiang Liu(刘荣香)1, and Xu-Hu Wang(王绪虎)1 |
1 College of Information and Control Engineering, Qingdao University of Technology, Qingdao 266520, China;
2 Department of Mathematics and Physics, and Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University, Baoding 071003, China |
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Abstract We study a generalized higher-order nonlinear Schrödinger equation in an optical fiber or a planar waveguide. We obtain the Lax pair and $N$-fold Darboux transformation (DT) with $N$ being a positive integer. Based on Lax pair obtained by us, we derive the infinitely-many conservation laws. We give the bright one-, two-, and $N$-soliton solutions, and the first-, second-, and $N$th-order breather solutions based on the $N$-fold DT. We conclude that the velocities of the bright solitons are influenced by the distributed gain function, $g(z)$, and variable coefficients in equation, $h_1(z)$, $p_1(z)$, $r_1(z)$, and $s_1(z)$ via the asymptotic analysis, where $ z $ represents the propagation variable or spatial coordinate. We also graphically observe that: the velocities of the first- and second-order breathers will be affected by $h_1(z)$, $p_1(z)$, $r_1(z)$, and $s_1(z)$, and the background wave depends on $g(z)$.
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Received: 30 August 2024
Revised: 19 September 2024
Accepted manuscript online: 24 September 2024
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PACS:
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02.30.Jr
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(Partial differential equations)
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42.50.Md
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(Optical transient phenomena: quantum beats, photon echo, free-induction decay, dephasings and revivals, optical nutation, and self-induced transparency)
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| Fund: Project supported by the the Fundamental Research Funds for the Central Universities (Grant No. 2023MS163). |
Corresponding Authors:
Xin Zhao
E-mail: zhaoxin@qut.edu.cn
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Cite this article:
Xin Zhao(赵鑫), Zhong Du(杜仲), Li-Jian Zhou(周立俭), Rong-Xiang Liu(刘荣香), and Xu-Hu Wang(王绪虎) Asymptotic analysis on bright solitons and breather solutions of a generalized higher-order nonlinear Schrödinger equation in an optical fiber or a planar waveguide 2024 Chin. Phys. B 33 110204
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[1] Marcuse D 2012 Principles of optical fiber measurements (Elsevier)
[2] Zhao X, Tian B, Zhang C R and Wang M 2022 Wave. Random Complex in press
[3] Mackenzie J I 2007 IEEE J. Sel. Top. Quant. 13 626
[4] Goban A, Hung C L, Hood J D, et al. 2015 Phys. Rev. Lett. 115 063601
[5] Degasperis A and Lombardo S 2013 Phys. Rev. E 88 052914
[6] Yi H H, Li X F, Zhang J L, Zhang X and Ma G L 2024 Chin. Phys. Lett. 33 100502
[7] Zhou Q, Zhong Y, Triki T, Sun Y Z, Xu S L, Liu W J and Biswas A 2022 Chin. Phys. Lett. 39 044202
[8] Yao Y L, Yi H H, Zhang X and Ma G L 2023 Chin. Phys. Lett. 40 100503
[9] Wang S B, Ma G L, Zhang X and Zhu D Y 2022 Chin. Phys. Lett. 39 114202
[10] Lan Z Z and Gao B 2017 Eur. Phys. J. Plus 132 512
[11] Hirota R 1973 J. Math. Phys. 14 805
[12] Ankiewicz A, Soto-Crespo J M and Akhmediev N 2010 Phys. Rev. E 81 046602
[13] Ding C C, Gao Y T, Deng G F and Wang D 2020 Chaos, Solitons Fract. 133 109580 |
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