On the growth and decay of transverse acceleration waves on a nonlinear, externally damped string

We examine the growth and decay of transverse acceleration waves on a nonlinear string whose motion takes place in a resisting medium. It is shown that one effect of external damping is to increase, with respect to the undamped case, the rate at which growth/decay of the waveʹs amplitude takes place. In addition, the effects of the stringʹs initial velocity are examined, a stability analysis is carried out, and a series of numerical simulations of acceleration waves on a finite string are presented.