Coupled long-Josephson junctions and the N sine-Gordon equation

The Lagrangians and equations of motion are derived for the junction phase differences for a family of coupled Josephson junction devices. These can be considered as the long junction versions and generalizations of the three-coupled Josephson device firs introduced by K.K. Likharev (1986). The possible two-field kink solutions for the long three-coupled Josephson junction device and three-field kinks for the long six-coupled junction device are derived. The two-field and three-field kinks are found to exist in equal mass families with SU(3) and SU(4) symmetries, respectively. With an external magnetic flux of the magnitude Φ=Φ₀/2 present, where Φ₀=h/2e is the flux quantum, the kinks of the three junction system have 1/3 and 2/3 fluxon subkinks that behave like quarks, e.g. exhibiting permanent confinement. A collective coordinate description and time-dependent one-dimensional numerical solutions for various kink collision, conversion, decay, and internal excitation processes are presented