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Some novel dynamical behaviours of localized solitary waves for the Hirota–Maccari system

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Abstract

This paper investigates a particular family of semi-rational solutions in determinant form by using the KP hierarchy reduction method, which describe resonant collisions among lumps or resemble line rogue waves and dark solitons in the Hirota–Maccari system. Due to the resonant collisions, the line resemble rogue waves are generated and attenuated in the background of dark solitons with line profiles of finite length, and it takes a short time for the lumps to appear from and disappear into the dark solitons background. These solitary waves have the characteristics of two-dimensional spatial localization and one-dimensional temporal localization that can be utilized to model two-dimensional rogue waves in many physical settings, such as oceanic rogue waves. Our results further cover some striking dynamic features in nonlinear localized waves propagation model.

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The data that support the findings of this article are available from the corresponding author upon reasonable request.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments and constructive suggestion. This work is supported by the National Natural Science Foundation of China (No. 11371326 and No. 11975145).

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  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Pei Xia, Yi Zhang, Heyan Zhang & Yindong Zhuang

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  1. Pei Xia
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Correspondence to Yi Zhang.

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Xia, P., Zhang, Y., Zhang, H. et al. Some novel dynamical behaviours of localized solitary waves for the Hirota–Maccari system. Nonlinear Dyn 108, 533–541 (2022). https://doi.org/10.1007/s11071-022-07208-w

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  • DOI: https://doi.org/10.1007/s11071-022-07208-w

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