All we know that the Burgers-KdV equation is extensively used to study the liquid flow with bubbles and the liquid moving flow in the elastic pipes. In this paper, we obtain the Lie point symmetries, self-nonlinear adjointness of a generalized Burgers-KdV equation (GB-KdVE) are obtained, it follows that the conservation laws are worked out. As a reduction of the GB-KdVE, a Burgers equation with general coefficients is presented, whose new strong symmetry and new nonlocal symmetries are generated, respectively. Furthermore, the noninvariant solutions of the GB-KdVE are produced as well. Finally, we propose the double linear differential constraints for GB-KdVE-type so that some soliton solutions are singled out.

中文翻译：

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广义 Burgers-KdV 方程的新对称性、群不变解、线性微分约束及其约简

我们都知道，Burgers-KdV 方程广泛用于研究带气泡的液体流动和弹性管中的液体移动流动。在本文中，我们得到李点对称性，得到广义Burgers-KdV方程（GB-KdVE）的自非线性伴随性，由此推导出守恒定律。作为GB-KdVE的简化，提出了具有一般系数的Burgers方程，分别产生了新的强对称性和新的非局部对称性。此外，还产生了 GB-KdVE 的非不变解。最后，我们提出了 GB-KdVE 类型的双线性微分约束，以便挑选出一些孤子解决方案。