Influence of impurities on hydrodynamic solitons

The interaction between impurities and solitary waves has been experimentally observed on the surface of a defective water layer subjected to vertical vibration. A slightly rugged surface on one sidewall of the water layer serves as the impurity, making the layer breadth at the defect slightly different elsewhere. A wide-breadth impurity will attract or pin not only the hydrodynamic breather at lower driving frequency, but also the kink at higher driving frequency, while a narrow-breadth one will repel them. Using a multiple scale expansion method, a nonlinear Schro dinger equation with an impurity term (NLSI) was derived from the basic hydrodynamic equation. Furthermore, we present numerical calculations that show good agreement between the NLSI-based theoretical model and the experimental results.