In this research, the general linear evolution equations (EEs) in (5+1) dimensions are studied. All the mixed second-order derivatives are included in this aforementioned model. Using the Hirota bilinear operator and symbolic computation, the localized solutions–the abundant lump solutions are constructed. Particularly, it is found that only four groups of linear (5+1)-dimensional EEs are found that they have abundant lump solutions, and no interactions between the lump and other solutions are found via the positive definite quadratic functions. Finally, four examples corresponding to the above-mentioned cases are given to validate the obtained results, and the corresponding graphs are presented to show the dynamic behaviors of the abundant lump solutions of these given examples.

在本研究中，研究了（5+1）维的一般线性演化方程（EE）。所有混合二阶导数都包含在上述模型中。使用 Hirota 双线性算子和符号计算，构建局部解——丰富的块解。特别地，发现只有四组线性(5+1)维EEs具有丰富的块解，并且通过正定二次函数没有发现块与其他解之间的相互作用。最后，给出了与上述案例相对应的四个例子来验证所获得的结果，并给出了相应的图表来显示这些给定例子的丰富块解的动态行为。