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Interactions among solitons for a fifth-order variable coefficient nonlinear Schrödinger equation

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Abstract

A fifth-order variable coefficient nonlinear Schrödinger equation based on original inhomogeneous model is proposed and studied. Bright multi-soliton analytic solutions of the equation are calculated through the Hirota method and auxiliary function. The effect of different constraints between fifth-order dispersion with third-order dispersion on soliton transmission is researched. Besides, their propagation and interaction dynamics are analyzed. Moreover, based on the obtained three-soliton solutions, we change the value of \(\beta (x)\) to discuss the soliton propagation. Three different propagation and interaction structures are derived via adjusting the nonlinear term. The results can enrich the inhomogeneous model and apply in nonlinear optical fiber.

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Acknowledgements

The work of Wenjun Liu was supported by the National Natural Science Foundation of China (11674036, 11875008, 91850209); Beijing Youth Top-notch Talent Support Program (2017000026833ZK08); Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications (IPOC2019ZZ01); and The Fundamental Research Funds for the Central Universities (500419305). This work was also funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia, under Grant No. (KEP-65-130-38). The authors, therefore, acknowledge with thanks DSR technical and financial support.

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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, China

    Suzhi Liu & Wenjun Liu

  2. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan, 430212, China

    Qin Zhou

  3. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL, 35762-7500, USA

    Anjan Biswas

  4. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Anjan Biswas & Abdullah Kamis Alzahrani

  5. Department of Applied Mathematics, National Research Nuclear University, Kashirskoe Shosse, Moscow, Russian Federation, 115409

    Anjan Biswas

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

    Anjan Biswas

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  1. Suzhi Liu
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  2. Qin Zhou
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  3. Anjan Biswas
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  4. Abdullah Kamis Alzahrani
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  5. Wenjun Liu
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Correspondence to Wenjun Liu.

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Liu, S., Zhou, Q., Biswas, A. et al. Interactions among solitons for a fifth-order variable coefficient nonlinear Schrödinger equation. Nonlinear Dyn 100, 2797–2805 (2020). https://doi.org/10.1007/s11071-020-05657-9

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