On the investigation of nonlinear waves of the Hirota and the Maxwell–Bloch equation in nonlinear optics

doi:10.1088/1674-1056/22/4/044208

中国物理B ›› 2013, Vol. 22 ›› Issue (4): 44208-044208.doi: 10.1088/1674-1056/22/4/044208

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

On the investigation of nonlinear waves of the Hirota and the Maxwell–Bloch equation in nonlinear optics

李传忠^a, 贺劲松^a,K. Porsezian^{b c}

a Department of Mathematics, Ningbo University, Ningbo 315211, China;
b Department of Physics, Pondicherry University, Puducherry 605014, India;
c Institute of Condensed Matter Theory and Solid State Optics, Friedrich-Schiller-Universität Jena, Max-Wein Platz 1, D-07743 Jena, Germany

收稿日期:2012-08-25 修回日期:2012-09-24 出版日期:2013-03-01 发布日期:2013-03-01
基金资助:
Project supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. LY12A01007), the National Natural Science Foundation of China (Grant Nos. 11201251, 10971109, and 11271210), K. C. Wong Magna Fund in Ningbo University, and K. Porseizan wishes to thank the DST, DAE-BRNS, UGC, and CSIR, Government of India, for the financial support through major projects.

On the investigation of nonlinear waves of the Hirota and the Maxwell–Bloch equation in nonlinear optics

Li Chuan-Zhong (李传忠)^a, He Jing-Song (贺劲松)^a, K. Porsezian^{b c}

a Department of Mathematics, Ningbo University, Ningbo 315211, China;
b Department of Physics, Pondicherry University, Puducherry 605014, India;
c Institute of Condensed Matter Theory and Solid State Optics, Friedrich-Schiller-Universität Jena, Max-Wein Platz 1, D-07743 Jena, Germany

Received:2012-08-25 Revised:2012-09-24 Online:2013-03-01 Published:2013-03-01
Contact: He Jing-Song E-mail:hejingsong@nbu.edu.cn
Supported by:
Project supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. LY12A01007), the National Natural Science Foundation of China (Grant Nos. 11201251, 10971109, and 11271210), K. C. Wong Magna Fund in Ningbo University, and K. Porseizan wishes to thank the DST, DAE-BRNS, UGC, and CSIR, Government of India, for the financial support through major projects.

摘要/Abstract

摘要： In this paper, considering the Hirota and Maxwell-Bloch (H-MB) equations which is governed by femtosecond pulse propagation through two-level doped fibre system, we construct the Darboux transformation of this system through linear eigenvalue problem. Using this Daurboux transformation, we generate multi-soliton, positon, and breather solutions (both bright and dark breathers) of the H-MB equations. Finally, we also construct the rogue wave solutions of the above system.

关键词: Hirota and Maxwell-Bloch equations, nonlinear optics, rogue wave

Abstract: In this paper, considering the Hirota and Maxwell–Bloch (H-MB) equations which is governed by femtosecond pulse propagation through two-level doped fibre system, we construct the Darboux transformation of this system through linear eigenvalue problem. Using this Daurboux transformation, we generate multi-soliton, positon, and breather solutions (both bright and dark breathers) of the H-MB equations. Finally, we also construct the rogue wave solutions of the above system.

Key words: Hirota and Maxwell–Bloch equations, nonlinear optics, rogue wave

中图分类号: (Optical solitons; nonlinear guided waves)

42.65.Tg

42.65.Sf (Dynamics of nonlinear optical systems; optical instabilities, optical chaos and complexity, and optical spatio-temporal dynamics) 05.45.Yv (Solitons) 02.30.Ik (Integrable systems)

李传忠, 贺劲松, K. Porsezian. On the investigation of nonlinear waves of the Hirota and the Maxwell–Bloch equation in nonlinear optics[J]. 中国物理B, 2013, 22(4): 44208-044208.

Li Chuan-Zhong (李传忠), He Jing-Song (贺劲松), K. Porsezian. On the investigation of nonlinear waves of the Hirota and the Maxwell–Bloch equation in nonlinear optics[J]. Chin. Phys. B, 2013, 22(4): 44208-044208.

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On the investigation of nonlinear waves of the Hirota and the Maxwell–Bloch equation in nonlinear optics

On the investigation of nonlinear waves of the Hirota and the Maxwell–Bloch equation in nonlinear optics

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