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

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 symmetry group method. Through generalized conditional method, this equation classified, considered are second, third, fourth, fifth-order, respectively. Meanwhile, equations transformed into system of ordinary differential solved.