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The local wave phenomenon in the quintic nonlinear Schrödinger equation by numerical methods

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Abstract

The nonlinear Schrödinger hierarchy has a wide range of applications in modeling the propagation of light pulses in optical fibers. In this paper, we focus on the integrable nonlinear Schrödinger (NLS) equation with quintic terms, which play a prominent role when the pulse duration is very short. First, we investigate the spectral signatures of the spatial Lax pair with distinct analytical solutions and their periodized wavetrains by Fourier oscillatory method. Then, we numerically simulate the wave evolution of the quintic NLS equation from different initial conditions through the symmetrical split-step Fourier method. We find many localized high-peak structures whose profiles are very similar to the analytical solutions, and we analyze the formation of rouge waves (RWs) in different cases. These results can be helpful to understand the excitation of nonlinear waves in some nonlinear fields, such as the Heisenberg ferromagnetic spin system in condensed matter physics, ultrashort pulses in nonlinear optical fibers, and so on.

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Data availability statement

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

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Acknowledgements

This research is supported by the National Natural Science Foundation of China (No. 11972291), Natural Science Basic Research Program of Shaanxi (No. 2020JM-115) and Aeronautical Science Foundation of China (No. 201941053004).

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  1. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, Shaanxi, 710129, People’s Republic of China

    Yaning Tang, Zaijun Liang & Wenxian Xie

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  1. Yaning Tang
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  2. Zaijun Liang
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Correspondence to Yaning Tang.

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Tang, Y., Liang, Z. & Xie, W. The local wave phenomenon in the quintic nonlinear Schrödinger equation by numerical methods. Nonlinear Dyn 108, 1547–1559 (2022). https://doi.org/10.1007/s11071-021-07169-6

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