Analytic solution for fluxons in a long Josephson junction with surface losses

Analytic solutions for a fluxon in a long Josephson junction in the presence of surface losses ($\beta$ term) as well as shunt losses ($\alpha$ term) are obtained by assuming a triangular current-phase relation. This theoretical result provides exact information on fluxon properties (e.g., the line shape, velocity, etc.), independent of the magnitude of $\alpha$ and $\beta$. We find that if $\beta$ is smaller than a critical value, the fluxon behavior is similar to that of the $\beta =0\mathrm{}$ case, but if $\beta$ is larger, quite different behavior is observed, particularly in the high-velocity region.