Lie symmetry analysis and exact explicit solutions of three-dimensional Kudryashov–Sinelshchikov equation

• All of the geometric vector fields of the equation are obtained.
• The symmetry reductions are presented.
• We obtain some new exact explicit solutions.

In this paper, the three-dimensional Kudryashov–Sinelshchikov (KS) equation, which describes the propagation of nonlinear waves in a bubbly liquid. By using the Lie symmetry analysis, all of the geometric vector fields of the equation are obtained, the symmetry reductions and some new exact explicit solutions are also presented.