A system with distributed nonlinearities: The array of Josephson junctions
Laboratoire de Mathématiques, INSA de Rouen, BP. 8, 76131 Mont-Saint-Aignan Cedex, France
2 Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise and CNRS, CNRS, France
We derive and review a new long wave model describing the electro-dynamics of point Josephson junctions in a superconducting cavity. It consists in a wave equation with Dirac delta function sine nonlinearities. This model allows a detailed and integrated description of the device that was not available up to now. In the static case, a remarkable agreement was obtained with experiments. For the dynamical behavior, three different solutions are identified: the ohmic mode, the junction mode and a dissipative kink. These have distinct signatures in the current voltage characteristics making them easy to identify in experiments.
© EDP Sciences, Springer-Verlag, 2007