Strongly nonlinear envelope soliton in a lattice model for periodic structure

Abstract

Nonlinear waves in a periodic structure are investigated numerically in terms of a modified Toda lattice model incorporating external linear elastic effect. The inclusion of the external linear elasticity causes a drastic change in wave properties, i.e. the wave packets, whose wavenumbers are determined by the relative importance of the external force to the internal force, play central roles instead of the Toda soliton. Numerically observed wave packets are well described by the nonlinear Schrödinger equation for weakly nonlinear regime, but an up-and-down asymmetry develops in the envelope for strongly nonlinear regime. The head-on collisions of such strongly nonlinear wave packets show their solitonic properties and that they can be considered as strongly nonlinear envelope solitons having an up-and-down asymmetry in amplitude.