The center of this paper is to establish the generalized variational structure (GVS) of the $(3+1)$-dimensional Zakharov–Kuznetsov–Burgers equation (ZKBe) by taking advantage of the Semi-inverse method (SIM). Two different GVSs are extracted and the derivation process is presented in detail. The extracted GVSs reveal the energy conservation law and can offer some new insights on the study of the variational method.

中文翻译：

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尘埃等离子体中 (3 + 1) 维 Zakharov-Kuznetsov-Burgers 方程的广义变分结构

本文的中心是建立广义变分结构（GVS）$（3+1）$利用半逆方法 (SIM) 的维 Zakharov–Kuznetsov–Burgers 方程 (ZKBe)。提取了两种不同的GVS并详细介绍了推导过程。提取的GVS揭示了能量守恒定律，可以为变分法的研究提供一些新的见解。