A general third order of linear partial differential equation in [Formula: see text] dimensions is studied by using the ansätz method. The lump solutions which localize in all directions in the whole [Formula: see text]-space are derived by the ansätz method. Diversity interactions including interacted lumps with periodic waves, interaction between lumps and multi-soliton, and interaction among lumps, multi-soliton and periodic waves are obtained by selecting the arbitrary functions. The phenomena of interaction between a lump and one-kink soliton, interaction between a lump and periodic waves, and interaction among a lump, one-kink soliton and periodic waves are analyzed by the three-dimensional plots and contour plots. The results may enrich the existing lump solutions in the [Formula: see text]-dimensional partial differential equations.

中文翻译：

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(3 + 1) 维偏微分方程中局域波与动态行为的相互作用

使用ansätz方法研究[公式：见文本]维度中的一般三阶线性偏微分方程。在整个 [公式：见正文] 空间中定位于所有方向的块解是通过 ansätz 方法得出的。通过选择任意函数，得到了包括团块与周期波的相互作用、团块与多孤子的相互作用以及团块、多孤子和周期波的相互作用的多样性相互作用。通过三维图和等高线图分析了团块与一扭结孤子的相互作用、团块与周期波的相互作用以及团块、一扭结孤子与周期波的相互作用等现象。该结果可能会丰富[公式：见正文]维偏微分方程中现有的块解。