junction array which is described by the standard discrete sine-Gordon equation. It is shown that there are compact fluxon and multi-fluxon states which either satisfy the top-bottom antisymmetry or are asymmetric. The anti-symmetric states have zero energy if their topological charge is even and the asymmetric states always have zero energy. Depending on the anisotropy constant the compact fluxons can either coexist with the non-compact states or only compact states are possible. External magnetic field prevents compact state existence.