Soliton decay in a Toda chain caused by dissipation

Consider a Toda chain with uniform friction. Starting with an initial condition that represents a soliton, we investigate its decay. The main result is that the solitary character is almost completely preserved.During the decay the wave activates other nonlinear modes. The corresponding actions appear to be bounded uniformly in time, proportional to the square of the friction coefficient.We focus upon the interaction with the same soliton but opposite direction of propagation. Comparing the numerical observations with an analytical model we conclude that the activated wave is well described by a linear equation, inhomogeneously driven by the main wave. The main wave itself decays as a nonlinear damped oscillator with one degree of freedom.