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

Behaviors of scattering soliton in a perturbed sine-Gordon equation system are 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 can be expressed as an exponential function e−βτ, where τ is the residence time. The value of β depends on the amplitude of external periodic force G. Such a dependence is expressed as β ~ (G − Gc)η, where Gc is a critical value defined as the value that the soliton cannot pass over the impurity. The value of the critical exponent η is determined from this relation and we obtain η = 0.328. This relation can be derived from an analysis based on the consideration of critical phenomenological behavior.