ON KINK-DYNAMICS OF THE PERTURBED SINE-GORDON EQUATION

The dynamics of 2 pi n-kink solutions to the perturbed sine-Gordon equ ation (PSGE), propagating with velocity c near unity is investigated. Using qualitative methods of differential equation theory and based on numerical simulations, we find that the dependence of the propagation velocity c on the bias parameter gamma has a spiral-like form in the (c, gamma)-plane in the neighborhood c=1 for all types of 2 pi n-kink solutions for appropriate values of the loss parameters in the PSGE. W e find numerically that the gamma-coordinates of the focal points, A(i ), of these ''spirals'' have a scaling property. So, it is possible to estimate the lower boundary of the parameter region where the 2 pi n- kink solutions to the PSGE can exist. The phase space structure at the points A(i) for the corresponding ODE system is also investigated. Th e form of 2 pi n-kink solutions in the neighborhood of the points A(i) is explained and the dynamics is discussed. A certain combination of the dissipative parameters of the PSGE is shown to be essential. The d ependence of the height of the zero field step of the long Josephson j unction modeled by the PSGE is also obtained.