In this work, the Date–Jimbo–Kashiwara–Miwa (DJKM) equation include time-dependent in $(2+1)$-dimensions that characterize the propagation of nonlinear dispersive waves in inhomogeneous media is studied. We construct rational solutions and the interaction physical phenomena between rational solution and multi-soliton wave to the time-dependent DJKM equation. The multi-soliton solutions are revealed by using the Hirota simple method, and then via the long-wave method, the M-lump solutions for two types of time-dependent are derived. Moreover, the interaction phenomena between rational solution and single-, double-soliton solutions are studied.

中文翻译：

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有理解，以及 (2 + 1) 维时间相关 Date–Jimbo–Kashiwara–Miwa 方程的交互解

在这项工作中，Date-Jimbo-Kashiwara-Miwa (DJKM) 方程包括时间相关的 $(2+1)$- 研究了表征非均匀介质中非线性色散波传播的维度。我们为瞬态 DJKM 方程构造有理解以及有理解与多孤子波之间的相互作用物理现象。利用Hirota简单方法揭示了多孤子解，然后通过长波方法，推导出了两种类型的时间依赖的M-lump解。此外，研究了有理解与单、双孤子解之间的相互作用现象。