In this paper, the (3+1)-dimensional defocusing Gardner-KP equation is investigated again with the help of Lie symmetry method since the results are either incorrect, or incomplete, or misleading in the literature. For the Lie algebra of infinitesimal symmetries spanned by eight vector fields, the one-dimensional optimal system of subalgebra is established by leveraging the fundamental invariants and general adjoint transformation representation. Meanwhile, by virtue of some infinitesimal generators in the optimal system, several symmetry reductions and exact solutions are presented.

中文翻译：

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(3+1)维散焦Gardner-KP方程的群分析和不变解


由于文献中的结果要么不正确，要么不完整，要么有误导性，本文借助李对称方法再次研究了（3+1）维散焦Gardner-KP方程。对于八个向量场的无穷小对称李代数，利用基本不变量和一般伴随变换表示建立一维最优子代数系统。同时，借助最优系统中的一些无穷小生成元，给出了几种对称性约简和精确解。