Surface solitons on elastic surfaces: numerics

Abstract

In previous work of the authors, the Whitam-Newell technique of study of small-amplitude, modulated, almost monochromatic signals was used to prove the existence of stable surface-wave solitary-like solutions of the envelope type on a structure made of a nonlinear elastic substrate and a superimposed elastic thin film. In the present work we present the results of numerical simulations performed either on the model one-dimensional nonlinear Schrödinger equation, or directly on the original two-dimensional elastic system using analytic solutions of the former as initial conditions in the latter. The numerical experiments confirm the solitary-wave behavior together with exponential decrease of amplitude with depth, as well as a very good solitonic behavior in the original mechanical system in the course of collision of the nonlinear surface waves. Surface elastic shock waves can also be exhibited when compensation between nonlinearity and dispersion is not precisely achieved.