NUMERICAL, EXPERIMENTAL, AND ANALYTICAL STUDIES OF THE DISSIPATIVE TODA LATTICE .1. THE BEHAVIOR OF A SINGLE SOLITARY WAVE

The time evolution of solitons in a dissipative Toda lattice has been studied numerically, and results have been compared with experimental data measured on a nonlinear electrical transmission line. In the absence of dissipation the Toda lattice is an integrable soliton system, but when dissipation is present the traveling solitary wave decreases and a tail is formed behind it. Nevertheless, some solitonic properties persist even with strong dissipation: There is some decreasing traveling wave solution which attracts all nearby initial conditions, furthermore the scattering of these solitary waves remains elastic, as will be shown in part II. For strong dissipation, and also for large times, the process is nonadiabatic and the perturbative methods used on the inverse scattering method do not seem to work. However, we have found a simple linear method for the construction of a good approximate solution for the dissipative tail. © 1990.