Optimal system, reductions and Lie algebra classification for Kudryashov–Sinelshchikov equations of second order

Abstract

In this work, the optimal system associated to the second order Kudryashov–Sinelshchikov equation is calculated. Such optimal system is obtained from the Lie symmetry group corresponding to the equation previously mentioned and using this algebra we are able to reduce this equation to known first order equations. In this way we find a new solutions, a wave travelling solution, which is represented graphically. Moreover, we classify the Lie algebra associated to the given equation.

Keywords

• Lie symmetry group
• Optimal system
• Lie algebra classification
• Kudryashov–Sinelshchikov equation