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Bright soliton solutions of the (2+1)-dimensional generalized coupled nonlinear Schrödinger equation with the four-wave mixing term

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Abstract

The (2+1)-dimensional generalized coupled nonlinear Schrödinger equation with the four-wave mixing (FWM) term is studied in this paper, which describes the optical solitons in a birefringent fiber. By virtue of the Hirota method, the one- and two-soliton solutions are derived. On the basis of solutions obtained, we discuss how the values of the FWM and some free parameters affect the solitons’ peformance. The FWM parameter can help to control the amplitude of the solitons. Meanwhile, by setting the values of certain free parameters, we can control the solitons’ propagation direction and speed, and reduce the interactions between them as well. In addition, the energy transfer of solitons during elastic collision and separation is also discussed. The conclusions here may be useful in improving the communication quality in multi-mode fibers.

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Acknowledgements

We acknowledge the financial support from the National Natural Science Foundation of China (Grant Nos. 11905009, 11875008, 12075034), by the Beijing Youth Top-notch Talent Support Program (Grant No. 2017000026833 ZK08), and by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications, Grant No. IPOC2017ZZ05).

Author information

Authors and Affiliations

  1. State Key Laboratory of Information Photonics and Optical Communications, P. O. Box 122, Beijing, China

    Lili Wang & Wenjun Liu

  2. School of Science, University of Posts and Telecommunications, Beijing, 100876, China

    Lili Wang & Wenjun Liu

  3. Beijing Union University, Beijing, 100101, China

    Zitong Luan

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

    Qin Zhou

  5. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80257, Jeddah, 21589, Saudi Arabia

    Qin Zhou

  6. Department of Physics, Chemistry and Mathematics, Alabama A & M University, Normal, AL, 35762–4900, USA

    Anjan Biswas

  7. Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Anjan Biswas

  8. Department of Applied Mathematics, National Research Nuclear University, 31 Kashirskoe Hwy, Moscow, –115409, Russian Federation

    Anjan Biswas

  9. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa–0204, Pretoria, South Africa

    Anjan Biswas

  10. Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Abdullah Kamis Alzahrani

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  1. Lili Wang
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  2. Zitong Luan
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Wang, L., Luan, Z., Zhou, Q. et al. Bright soliton solutions of the (2+1)-dimensional generalized coupled nonlinear Schrödinger equation with the four-wave mixing term. Nonlinear Dyn 104, 2613–2620 (2021). https://doi.org/10.1007/s11071-021-06411-5

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