We consider a long Josephson junction with alternating 0- and $\pi$-facets with different facet lengths between the 0- and the $\pi$-parts. Depending on the combinations between the 0- and the $\pi$-facet lengths, an antiferromagnetically ordered semifluxons array can be the ground state of the system. Due to the fact that in that case there are two independent ground states, an externally introduced 2$\pi$ fluxon will be splintered or fractionalized. The magnitude of the flux in the fractional fluxons is a function of the difference between the 0 and the $\pi$-facet lengths. Here, we present an analytical calculation of the flux of splintered Josephson fluxons for any combination of 0- and $\pi$-facet lengths. In the presence of an applied bias current, we show numerically that only one of the two fractional fluxons can be moved. We also consider the I–V characteristics of the ground state and the one of a 2$\pi$-fluxon in a zig-zag junction.
Susanto, H., Darminto, D., Darminto, U., & van Gils, S. A. (2007). Static and dynamic properties of fluxons in a zig-zag 0-π Josephson junction. Physics letters A, 361(7/3), 270-276. [10.1016/j.physleta.2006.09.044]. https://doi.org/10.1016/j.physleta.2006.09.044