Bifurcation Analysis and Numerical Study of Wave Solution for Initial-Boundary Value Problem of the KdV-BBM Equation

Abstract

In this work, we study the bifurcation and the numerical analysis of the nonlinear Benjamin-Bona-Mahony-KdV equation. According to the bifurcation theory of a dynamic system, the various kinds of traveling wave profiles are obtained including the behavior of solitary and periodic waves. Additionally, a two-level linear implicit finite difference algorithm is implemented for investigating the Benjamin-Bona-Mahony-KdV model. The application of a priori estimation for the approximate solution also provides the convergence and stability analysis. It was demonstrated that the current approach is singularly solvable and that both time and space convergence are of second-order precision. To confirm the computational effectiveness, two numerical simulations are prepared. The findings show that the current technique performs admirably in terms of delivering second-order accuracy in both time and space with the maximum norm while outperforming prior schemes.