In this work, we study a generalised (2+1) equation of the Zakharov–Kuznetsov (ZK)(m,n,k) equation involving three arbitrary functions. From the point of view of the Lie symmetry theory, we have derived all Lie symmetries of this equation depending on the arbitrary functions. Line soliton solutions have also been obtained. Moreover, we study the low-order conservation laws by applying the multiplier method. This family of equations is rich in Lie symmetries and conservation laws. Finally, when the equation is expressed in potential form, it admits a variational structure in the case when two of the arbitrary functions are linear. In addition, the corresponding Hamiltonian formulation is presented.

中文翻译：

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Zakharov-Kuznetsov 方程族在 2 1 维+中的李对称性和低阶守恒定律

在这项工作中，我们研究了涉及三个任意函数的 Zakharov-Kuznetsov (ZK)(m,n,k) 方程的广义 (2+1) 方程。从李对称理论的角度来看，我们已经根据任意函数导出了该方程的所有李对称。还获得了线孤子解决方案。此外，我们通过应用乘法器方法研究低阶守恒定律。这一系列方程具有丰富的李对称性和守恒定律。最后，当方程以势形式表示时，在任意两个函数是线性的情况下，它允许变分结构。此外，还给出了相应的哈密顿公式。