Microscopic tunneling theory of long Josephson junctions

We present a numerical scheme for solving a nonlinear partial integro-differential equation with nonlocal time dependence. The equation describes the dynamics in a long Josephson junction modeled by use of the microscopic theory for tunneling between superconductors. We demonstrate that the detailed behavior of a solitonic mode (fluxon dynamics) in the junction is different from the results of the conventional perturbed sine-Gordon model.