| ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS |
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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. Porsezianb 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 |
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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.
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Received: 25 August 2012
Revised: 24 September 2012
Accepted manuscript online:
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PACS:
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42.65.Tg
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(Optical solitons; nonlinear guided waves)
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42.65.Sf
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(Dynamics of nonlinear optical systems; optical instabilities, optical chaos and complexity, and optical spatio-temporal dynamics)
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05.45.Yv
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(Solitons)
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02.30.Ik
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(Integrable systems)
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| Fund: 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. |
Corresponding Authors:
He Jing-Song
E-mail: hejingsong@nbu.edu.cn
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Cite this article:
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 2013 Chin. Phys. B 22 044208
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