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Formation and propagation dynamics of peakons and double-hump solitons of the generalized focusing/defocusing NLS equations with \(\varvec{\mathcal{P}\mathcal{T}}\)-symmetric \(\varvec{\delta }{} \mathbf{(x)}\)-sech optical potentials

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Abstract

In this paper, we investigate several important properties of the generalized nonlinear Schrödinger equation with \(\mathcal{P}\mathcal{T}\)-symmetric \(\delta \)-sech optical potentials, such as the phase breaking of \(\mathcal{P}\mathcal{T}\)-symmetric \(\delta \)-sech potentials, and existence, dynamics and excitations of new soliton solutions. Specifically, we identify the fully real spectral region of the non-Hermitian Hamiltonian and observe the phase-breaking phenomenon. Additionally, we discover a new soliton solution that represents a peakon solution, a smooth soliton solution, and a double-hump soliton solution under different potential parameters. We analyze the stability of these three types of solutions and determine their stability domains. Furthermore, we study the numerical peakon solution and its stability. In particular, we investigate the interaction of peakon solutions and observe semi-elastic interactions. Finally, we explore the stable adiabatic excitations of peakons. These results contribute to a deeper understanding of \(\mathcal{P}\mathcal{T}\)-symmetric optical fields and provide insights for related experimental works.

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Funding

The work was supported by the National Natural Science Foundation of China (No. 11925108).

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Zijian Zhou

  2. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, China

    Yong Chen

  3. KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Zhenya Yan

  4. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Zhenya Yan

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  1. Zijian Zhou
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Correspondence to Zhenya Yan.

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Zhou, Z., Chen, Y. & Yan, Z. Formation and propagation dynamics of peakons and double-hump solitons of the generalized focusing/defocusing NLS equations with \(\varvec{\mathcal{P}\mathcal{T}}\)-symmetric \(\varvec{\delta }{} \mathbf{(x)}\)-sech optical potentials. Nonlinear Dyn 112, 6597–6613 (2024). https://doi.org/10.1007/s11071-024-09346-9

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