In this paper, a (2 + 1)-dimensional variable-coefficients Calogero–Bogoyavlenskii–Schiff (vcCBS) equation is studied. The infinitesimal generators and symmetry groups are obtained by using the Lie symmetry analysis on vcCBS. The optimal system of one-dimensional subalgebras of vcCBS is computed for determining the group-invariant solutions. On this basis, the vcCBS is reduced to two-dimensional partial differential equations (PDEs) by similarity reductions. Furthermore, the reduced PDEs are solved to obtain the two-soliton interaction solution, the soliton-kink interaction solution and some other exact solutions by the (G′ G )-expansion method. Moreover, it is shown that vcCBS is nonlinearly self-adjoint and then its conservation laws are calculated.

中文翻译：

---

Lie 对称性分析、精确解、变系数 Calogero–Bogoyavlenskii–Schiff 方程的守恒定律

在本文中，一个(2 + 1)研究了维变量系数Calogero-Bogoyavlenskii-Schiff (vcCBS) 方程。通过对vcCBS进行李对称分析，得到了无穷小的生成元和对称群。计算vcCBS的一维子代数的最优系统以确定群不变解。在此基础上，vcCBS 通过相似性减少简化为二维偏微分方程 (PDE)。此外，通过求解简化的偏微分方程，得到双孤子相互作用解、孤子-扭结相互作用解和其他一些精确解(G' G )- 扩展方法。此外，证明了vcCBS是非线性自伴随的，然后计算了它的守恒定律。