Analysis And Simulation Of Periodic And Solitary Waves In Nonlinear Dispersive-Dissipative Solids

In this paper, we consider a general realistic nonlinear elastic rod model which is embedded in an external medium with weak disturbance. We apply the geometric singular perturbation theory to prove the existence of a unique periodic traveling wave in this model. With a dynamical system approach, it is shown that the periodic wave appears near a stationary state and then amplifies and degenerates into a solitary wave. Simulations are presented to demonstrate an excellent agreement with the theoretical predictions. (c) 2021 Elsevier B.V. All rights reserved.