Perturbation of traveling Boussinesq solitons by periodic bathymetry

Nonlinear waves over varying topography remain important topics in oceanographic applications. Modeling solitons over a variable seabed is more challenging than modeling waves on a flat surface, where integrable autonomous equations, such as the Korteweg-de Vries equation, are effective. The geometric complexity of the bathymetry leads to non-integrable, non-autonomous nonlinear systems. We map the perturbations caused by periodic bathymetry on Boussinesq solitons into a perturbed KdV equation and compare our analytical solutions and their stability with numerical simulation across different parameters related to nonlinearity, dispersion, and bathymetry.