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Instability dynamics of Peregrine soliton revisited with a modal expansion technique

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Abstract

In this paper, we aim at taking a step towards exploring the unstable dynamics of Peregrine soliton as a prototype of rogue waves. Given its spatio-temporal doubly localized structure, the generic Fourier-spectral scheme fails to realize the dimensionality reduction of its nonlinear dynamics. We introduce a modal expansion technique in which physical properties of wave structure are mapped onto proper orthogonal modal basis with space-independent. As a result, the evolution of Peregrine soliton is reduced to an equivalent particle motion in 3-dimension phase space. The govern equation obtained can not only capture correctly underlying behaviors as well as transient natures, but also reveal nicely a complex and subtle structure of the unstable process within the phase-space representation. High consistency with the reconstructed field and the theoretical solution validate the reliability and feasibility of the approach.

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Acknowledgements

This work was supported by the National Science Foundation of China (NSFC) (61975130), and by Guangdong Basic and Applied Basic Research Foundation (2021A1515010084).

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Authors and Affiliations

  1. International Collaborative Laboratory of 2D Materials for Optoelectronics Science and Technology, Institute of Microscale Optoelectronic, Shenzhen University, Shenzhen, 518060, China

    Zhixiang Deng, Dianyuan Fan & Lifu Zhang

  2. School of Electronic and Communication Engineering, Guiyang University, Guiyang, 550005, China

    Jin Zhang

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  1. Zhixiang Deng
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  2. Jin Zhang
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Correspondence to Zhixiang Deng.

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Deng, Z., Zhang, J., Fan, D. et al. Instability dynamics of Peregrine soliton revisited with a modal expansion technique. Nonlinear Dyn 111, 15373–15380 (2023). https://doi.org/10.1007/s11071-023-08675-5

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