In this paper, we investigate the (2 + 1)-dimensional Hirota–Satsuma–Ito (HSI) shallow water wave model. By introducing a small perturbation parameter $ϵ$, an extended (2 + 1)-dimensional HSI equation is derived. Further, based on the Hirota bilinear form and the Hermitian quadratic form, we construct the rational localized wave solution and discuss its dynamical properties. It is shown that the oblique and skew characteristics of rational localized wave motion depend closely on the translation parameter $ϵ$. Finally, we discuss two different interactions between a rational localized wave and a line soliton through theoretic analysis and numerical simulation: one is an absorb-emit interaction, and the other one is an emit-absorb interaction. The results show that the delay effect between the encountering and parting time of two localized waves leads to two different kinds of interactions.

中文翻译：

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（2 1）维Hirota-Satsuma-Ito方程中的有理局部波及其吸收发射相互作用

在本文中，我们研究了（2 +1）维Hirota–Satsuma–Ito（HSI）浅水波模型。通过引入一个小的扰动参数$ϵ$，导出一个扩展的（2 +1）维HSI方程。此外，基于Hirota双线性形式和Hermitian二次形式，构造有理局域波解并讨论其动力学性质。结果表明，合理局部波动的倾斜和偏斜特性与平移参数密切相关。$ϵ$。最后，我们通过理论分析和数值模拟讨论了有理局域波和线孤子之间的两种不同相互作用：一种是吸收－吸收相互作用，另一种是发射－吸收相互作用。结果表明，两个局部波的相遇和分离时间之间的延迟效应导致两种不同类型的相互作用。