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Soliton resonances, soliton molecules, soliton oscillations and heterotypic solitons for the nonlinear Maccari system

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Abstract

Soliton resonances and soliton molecules have become a hot topic in the field of nonlinear science and engineering in recent years due to their potential applications. This work presents a systematic study of the soliton interaction dynamics of the Maccari system. Using the bilinear method, explicit first- and second-order solutions of the system are derived for the system. With these solutions and carefully chosen parameters, we observe various soliton interaction phenomena, such as soliton resonances, soliton molecules, soliton oscillations, and heterotypic solitons, including the V- and Y-type soliton, for the two dependent variables under two coordinate systems: space and spatiotemporal coordinate systems, respectively. Notably, we find that soliton molecules and heterotypic solitons exhibit completely different features under the two coordinate systems. The constraint conditions for the existence of soliton molecules are more restrictive in the spatiotemporal coordinate, and the occurrence of V- and Y-type soliton patterns is relatively rare in this coordinate system.

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Technology and Business University, Beijing, 100048, China

    Yu-Lan Ma

  2. Department Mathematics, Saint Xavier University, Chicago, IL, 60655, USA

    Abdul-Majid Wazwaz

  3. School of Computer Science and Engineering, Beijing Technology and Business University, Beijing, 100048, PR, China

    Bang-Qing Li

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  1. Yu-Lan Ma
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  2. Abdul-Majid Wazwaz
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  3. Bang-Qing Li
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Contributions

Yu-Lan Ma: Conceptualization, Software, Validation, Writing - review and editing, Methodology. Abdul-Majid Wazwaz: Conceptualization, Methodology. Bang-Qing Li: Methodology, Formal analysis, Data curation, Writing - original draft.

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Correspondence to Bang-Qing Li.

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Ma, YL., Wazwaz, AM. & Li, BQ. Soliton resonances, soliton molecules, soliton oscillations and heterotypic solitons for the nonlinear Maccari system. Nonlinear Dyn 111, 18331–18344 (2023). https://doi.org/10.1007/s11071-023-08798-9

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