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Analytic study on interactions between periodic solitons with controllable parameters

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Abstract

Soliton interactions occur when two solitons are close enough. In general, periodic oscillations can be presented during soliton interactions. The periodic oscillations will lead to the soliton distortion, which is necessary to carry out the effective control. In this paper, interactions between periodic solitons with controllable parameters are investigated analytically. One- and two-soliton solutions for the nonlinear Schrödinger equation are derived by using the Hirota’s bilinear method. According to analytic solutions, the influences of each parameter on period interactions between solitons are discussed, and the method of how to control the cycle of interactions is suggested. Results in this paper can be used for the theoretical guidance of how to make the soliton transmission more efficient and more fidelity, and are of great significance for optical fiber communications.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11674036), by the Beijing Youth Top-notch Talent Support Program (Grant No. 2017000026833ZK08) and by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications, Grant Nos. IPOC2016ZT04 and IPOC2017ZZ05). This work of Qin Zhou was supported by the National Natural Science Foundation of China (Grant Nos. 11705130 and 1157149), and this author was also sponsored by the Chutian Scholar Program of Hubei Government in China.

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Authors and Affiliations

  1. State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, P. O. Box 122, Beijing, 100876, People’s Republic of China

    Xiaoyan Liu & Wenjun Liu

  2. Radiation Physics Laboratory, Department of Physics, Faculty of Sciences, Badji Mokhtar University, P. O. Box 12, 23000, Annaba, Algeria

    Houria Triki

  3. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan, 430212, People’s Republic of China

    Qin Zhou

  4. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL, 35762, USA

    Anjan Biswas

  5. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Anjan Biswas

  6. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria, 0008, South Africa

    Anjan Biswas

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  1. Xiaoyan Liu
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  2. Houria Triki
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Correspondence to Qin Zhou or Wenjun Liu.

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Liu, X., Triki, H., Zhou, Q. et al. Analytic study on interactions between periodic solitons with controllable parameters. Nonlinear Dyn 94, 703–709 (2018). https://doi.org/10.1007/s11071-018-4387-7

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