Numerical simulation of sine-Gordon soliton dynamics in the presence of perturbations

摘要: We have developed a computer simulation program to study the dynamical behavior of soliton solutions sine-Gordon equation in presence external perturbations. Our work extends numerical and formal mathematical analysis on system four directions. First, we demonstrate that lossless propagation lattice is complicated by pinning effect generation "harmonic excitations" as "radiation." define regimes according coefficient ${\ensuremath{\omega}}_{0}^{2}$ nonlinear potential term which can (${\ensuremath{\omega}}_{0}^{2}\ensuremath{\lesssim}1$) or cannot (${\ensuremath{\omega}}_{0}^{2}\ensuremath{\gtrsim}1$) occur. Second, two examples perturbation are particular importance condensed matter: (i) model impurity binds low-velocity solitons but merely space shifts those with high velocities, (ii) spatial inhomogeneities cause adjust its velocity shape regions imperfection. find results Fogel et al., who treat these types linear theory, accurate better than 25% long small parameter does not exceed 0.1. Third their conclusion be treated classical $\ensuremath{\phi}$ particles obeying Newton's laws excellent agreement results. Finally indicate several applications our for quantum flux along Josephson-junction transmission line.