Abstract
Polynomial and rational wave solutions of Kudryashov-Sinelshchikov equation and numerical simulations for its dynamic motions are investigated. Conservation flows of the dynamic motion are obtained utilizing multiplier approach. Using the unified method, a collection of exact solitary and soliton solutions of Kudryashov-Sinelshchikov equation is presented. Collocation finite element method based on quintic B-spline functions is implemented to the equation to evidence the accuracy of the proposed method by test problems. Stability analysis of the numerical scheme is studied by employing von Neumann theory. The obtained analytical and numerical results are in good agreement.