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Solitons, Breathers and Modulation Instability for a Higher-Order Coupled Nonlinear Schrödinger System for the Ultrashort Optical Pulses in a Nonlinear Medium

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Abstract

In this paper, we investigate some soliton and breather solutions for a higher-order coupled nonlinear Schrödinger system which may describe the ultrashort optical pulses in a nonlinear medium. With the help of the existing Darboux transformation, we construct the first- and second-order soliton solutions, as well as the first- and second-order breather solutions. We present two types of the solitons, i.e., two-hump solitons and one-hump solitons. Interaction between the two one-hump solitons, and interaction between a two-hump soliton and a one-hump soliton are presented. When the velocities of two solitons are equal, we obtain the bound state of the two solitons. Real constant \(\varepsilon \) in the system affects the velocities of the solitons. We show the one breather and interaction between the two breathers. Velocities and shapes of the breathers are also affected by \(\varepsilon \). We discuss the modulation instability of that system through the linear stability analysis. That system may describe the ultrashort optical pulses in a nonlinear medium, therefore the wave phenomena proposed in our paper may provide certain theoretical references for the related experiments in the future.

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The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

We express our sincere thanks to the Editors and Reviewers for their valuable comments. This work has been supported by the National Natural Science Foundation of China under Grant Nos. 11772017, 11272023 and 11471050, by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05), by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02 and by the BUPT Excellent Ph.D. Students Foundation (Nos. CX2022312 and CX2022156).

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  1. State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Dan-Yu Yang, Bo Tian, Yuan Shen & Xiao-Tian Gao

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  1. Dan-Yu Yang
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Yang, DY., Tian, B., Shen, Y. et al. Solitons, Breathers and Modulation Instability for a Higher-Order Coupled Nonlinear Schrödinger System for the Ultrashort Optical Pulses in a Nonlinear Medium. Qual. Theory Dyn. Syst. 22, 59 (2023). https://doi.org/10.1007/s12346-022-00728-1

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