The analytical solutions of a nonlinearly coupled sine-Gordon system of equ
ations are discussed. The relevant solutions are then used as a basis for t
he numerical analysis of a perturbed sine-Gordon system of equations modeli
ng a cell of three long Josephson junctions. The analysis is focused on the
dynamical states accounting for the current singularities, in the absence
as well as in the presence of magnetic held, at the relevant values of the
magnetic flux linked to the cell (Phi= 0 and Phi=Phi(0)/2). The experimenta
l evidence for zero-field and flux-flow steps in the device is also discuss
ed. [S0163-1829(99)04721-9].