Effective behavior of solitary waves over random topography

摘要: The deformation of a nonlinear pulse traveling in dispersive random medium can be studied with asymptotic analysis based on separation scales when the propagation distance is large compared to correlation length medium. We consider shallow water waves spatially depth. use formulation terms terrain-following Boussinesq system. compute effective evolution equation for front which written as dissipative Kortweg-de Vries equation. study soliton dynamics driven by this show, both theoretically and numerically, that solitary wave more robust than linear early steps propagation. However, it eventually decays much faster after critical corresponding loss about half its initial amplitude. also perform an class bottom topographies. A universal behavior captured through metric term change coordinates. Within we characterize height highly disordered probabilistic results are illustrated performing Monte Carlo simulations Schwarz-Christoffel Toolbox.