COUPLED LONG JOSEPHSON-JUNCTIONS AND THE N SINE-GORDON EQUATION

We derive the Lagrangians and equations of motion 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 first introduced by Likharev. 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 having SU(3) and SU(4) symmetries respectively. With an external magnetic flux present of magnitude phi = PHI-o/2, where PHI-o = h/2e is the flux quantum, the kinks of the 3 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.