Effect of diffusion parameters on traveling wave solutions of singular perturbed Boussinesq equation

Abstract

This paper focuses on the nature of the traveling wave solutions of the singular perturbed (sixth-order) Boussinesq equation, which is important for the physical relationships of water waves and shows strong interactions. Most studies of this equation have been analyzed by numerical methods and it has been observed that analytical solutions are limited. This has formed the main motivation for an analytical method, the Kudryashov method, for the generation of traveling wave solutions. One of the important goals of this work is to analyze the wave propagation phenomena in detail. For this purpose, the model has been extended by adding parameters to the diffusion term, which can illuminate shallow fluid layers and nonlinear atomic phenomena. This model aims to provide a deeper understanding of the motion of waves and the behavior of fluids, as well as its solution by the analytical method. To deepen the physical discussion, the responses of the solution are simulated for different values of the diffusion coefficient and the parameter associated with the wave velocity.