Invariant Subspace and Exact Solutions to the Generalized Kudryashov-Sinelshchikov Equation (Journal of Partial Differential Equations, 2023)
In this research, invariant subspaces and exact solutions for the governingequation are obtained through the invariant subspace method, and the generalizedsecond-order Kudryashov-Sinelshchikov equation is used to describe pressure wavesin a liquid with bubbles. The governing equations are classified and transformed intoa system of ordinary differential equations, and the exact solutions of the classifiedequation are obtained by solving the system of ordinary differential equations. Themethod gives logarithmic, polynomial, exponential, and trigonometric solutions forequations. The primary accomplishments of this work are displaying how to obtain theexact solutions of the classified equations and giving the stability analysis of reducedordinary differential equations.
Keywords: Invariant subspace method; exact solution; Kudryashov-Sinelshchikov equation; stability analysis.