Symmetry Classification and Solutions for the Third-Order of Kudryashov–Sinelshchikov Equation

Abstract

This paper studies nonlinear wave propagation in a bubble-liquid mixture based on the third-order Kudryashov–Sinelshchikov (KS) equation. Symmetry is classified and reduced through the symmetry group method. Through the generalized conditional symmetry method, this equation is classified, and the generalized conditional symmetry considered are second, third, fourth, and fifth-order, respectively. Meanwhile, the classified equations are transformed into a system of ordinary differential equations and solved.