Abstract
A quantum flux, a 2π fluxon, described by a sine-Gordon equation is an elementary excitation in long Josephson junctions. We investigated the fluxon dynamics in isolated long Josephson junctions. In such isolated systems, the total number of Cooper pairs is conserved, so the fluxon dynamics may change. We found that the fluxons obey a double sine-Gordon (DSG) equation based on this change in the Josephson acceleration relation, i.e., the voltage-phase difference relation. It should be possible to confirm the existence of DSG fluxons by detecting the relative oscillations of two π fluxons.
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