Linear and nonlinear excitations in two stacks of parallel arrays of long Josephson junctions

We investigate a structure consisting of two parallel arrays of long Josephson junctions sharing a common electrode that allows inductive coupling between the arrays. A model for this structure is derived starting from the description of its continuous limit. The excitation of linear cavity modes known from continuous and discrete systems as well as the excitation of a new state exhibiting synchronization in two dimensions are inferred from the mathematical model of the system. The stable nonlinear solution of the coupled sine-Gordon equations describing the system is found to consist of a fluxon-antifluxon string. This is a two-dimensional phase-locked solitonic mode. Both linear and nonlinear excitations are numerically investigated and experimentally demonstrated in two stacks of five-junction arrays.