A new perspective for analytical and numerical soliton solutions of the Kaup–Kupershmidt and Ito equations

Abstract

In present study, it is aimed to implement the analytical method and a numerical approach based on finite element method to get approximate soliton solutions of two special forms of fifth-order KdV equation (fKdV) that are of particular importance: Kaup–Kupershmidt (K–K) and Ito equations. To reach these aims, the simplest equation method and septic B-spline collocation method are introduced. L2 and L∞ error norms are computed for single soliton solutions to demonstrate the proficiency and accuracy of the present method. The method is shown to be unconditionally stable by performing the von-Neumann stability analysis. The obtained numerical results have been displayed with tables. Additionally, to show the analytical and numerical behaviors of the single soliton, all figures are drawn in 2D and 3D. Analytical and numerical results ensure that the methods are more suitable and systematically handle the solution procedures of nonlinear equations arising in mathematical physics.