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Dynamics of soliton resonances and soliton moleculesfor the AB system in two-layer fluids

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Abstract

The AB system is a critical component of fluid dynamics, as it is capable of modeling the nonlinear wave motions in two-layer fluids. In this study, we investigate soliton molecules and soliton resonance in the AB system. We employ the Darboux transformation scheme to derive new, explicit expressions for one- to four-order soliton solutions for the system. These solutions include spectrum parameter allowing us to explore novel soliton resonances and soliton molecules in the system. We identify two types of soliton resonances: local and global. We also reveal the evolution dynamics from local to global resonances. Global soliton resonances can be understood as the limit of local soliton resonances. Additionally, based on both the phase parameters, we report the existence of soliton molecules in the AB system. We further discover that parallel soliton molecules without entanglement become global soliton resonances with entanglement as the phase parameters approach zero. This finding holds great significance for the system as it provides theoretical evidence that the system possesses a breather-like wave structure, where two or multiple solitons exhibit mutual entanglement and stable energy. These findings enhance our understanding of the AB system and shed light how to manage and control these stable resonant solitons.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Technology and Business University, Beijing, 100048, People’s Republic of China

    Yu-Lan Ma

  2. School of Computer Science and Engineering, Beijing Technology and Business University, Beijing, 100048, People’s Republic of China

    Bang-Qing Li

  3. Academy of Systems Science, Beijing Technology and Business University, Beijing, 100048, People’s Republic of China

    Bang-Qing Li

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Y-LM contributed to conceptualization, validation, writing—review and editing, and methodology and provided software. B-QL was involved in methodology, formal analysis, data curation and writing—original draft.

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Ma, YL., Li, BQ. Dynamics of soliton resonances and soliton moleculesfor the AB system in two-layer fluids. Nonlinear Dyn 111, 13327–13341 (2023). https://doi.org/10.1007/s11071-023-08529-0

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