Initial condition dependence of the residence time for scattering soliton in a perturbed sine-Gordon equation system (Q1809563)

The behavior of a scattering soliton in a perturbed sine-Gordon equation system is numerically studied. We measure the residence time which is defined as the time that the soliton is trapped by an impurity. The initial condition dependence of the residence time has a self-similar fractal structure and the distribution function of the residence time \(\tau\) can be expressed as an exponential function \(e^{-\beta\tau}\).