On Lie symmetries, optimal systems and explicit solutions to the Kudryashov–Sinelshchikov equation

Under investigation in this paper is the Kudryashov–Sinelshchikov equation, which describes influence of viscosity and heat transfer on propagation of the pressure waves. The Lie symmetry method is used to study its vector fields and optimal systems, respectively. Furthermore, the symmetry reductions and exact solutions of the equation are obtained on the basic of the optimal systems. Finally, based on the power series theory, a kind of explicit power series solutions for the equation is well constructed with a detailed derivation.