A direct and effective method is employed to construct the discrete models of high-dimensional generalized Zakharov–Kuznetsov and diffusion–convection equations. Through the compatibility condition, we construct their potential systems, whose local symmetries can be projected into the local and nonlocal symmetries of the original equations. Furthermore, based on the resulting Lie symmetries, the invariant difference models and symmetry-preserving difference models of the original two equations can be derived by using the orthogonal meshes which are uniform in space. Finally, some exact solutions of these two equations are also obtained with their graphic analysis.

中文翻译：

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某些高维微分方程的保持对称性的差分格式和精确解

采用直接有效的方法来构造高维广义Zakharov-Kuznetsov方程和扩散-对流方程的离散模型。通过相容条件，我们构造了它们的潜在系统，其局部对称性可以投影到原始方程的局部和非局部对称性中。此外，基于产生的李对称性，可以使用空间均匀的正交网格来推导原始两个方程的不变差分模型和保持对称性的差分模型。最后，还通过图形分析获得了这两个方程的精确解。