Two-layer fluid models are used to depict some nonlinear phenomena in fluid mechanics, medical science and thermodynamics. In this paper, we investigate a (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation for the interfacial waves in a two-layer liquid or elastic quasiplane waves in a lattice. Via the Kadomtsev-Petviashvili hierarchy reduction, we derive the rational solutions in the determinant forms and semi-rational solutions. The nth-order lump waves and multi-lump waves are obtained, where n is a positive integer. We observe the second-order lump waves: Two-lump waves interact with each other and separate into two new lump waves. Two-lump waves are observed: Overtaking interaction takes place between the two-lump waves; After the interaction, the two-lump waves propagate with their original velocities and amplitudes. Studying the semi-rational solutions, we show the fusion between a lump wave and a bell-type soliton and fission of a bell-type soliton. Interaction between a line rogue wave and a bell-type soliton is shown.

中文翻译：

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液体或晶格中 (3+1) 维 Yu-Toda-Sasa-Fukuyama 方程的流氓波和团波

两层流体模型用于描述流体力学、医学和热力学中的一些非线性现象。在本文中，我们研究了一个（3+1) 用于两层液体中的界面波或晶格中的弹性准平面波的一维 Yu-Toda-Sasa-Fukuyama 方程。通过 Kadomtsev-Petviashvili 层次化约简，我们推导出行列式形式的有理解和半有理解。这n得到了三阶团波和多团波，其中n是一个正整数。我们观察到二阶团波：两个团波相互作用并分离成两个新的团波。观察到两团波：两团波之间发生超车相互作用；相互作用后，两团波以其原始速度和振幅传播。研究半有理解，我们展示了团波与钟形孤子的融合以及钟形孤子的裂变。显示了线流氓波和钟型孤子之间的相互作用。