We study quasi-one-dimensional arrays of inductively coupled Josephson junctions with only self-inductance of a cell taken into account. A 2-row anisotropic Josephson junction ladder (JJL) has a flat band in the linear electromagnetic wave spectrum . We derive the equations of motion for a 3-row anisotropic JJL and generalise them for a ladder with an arbitrary number of rows $ \kappa \geq 3 $. In the case of weak damping we obtain the spectrum of linear electromagnetic waves in these arrays. A $ \kappa $-row JJL has 3 bands in the spectrum, two of them are dispersive: the upper band consists of $ (\kappa-1) $ branches, the lower one of 2 branches, the band in the middle of the spectrum is dispersionless (flat) and is $ (\kappa - 2) $-fold degenerate. At zero external dc bias current the two lower branches become flat, resulting in $ \kappa $-fold degeneracy of the flat band.
The Authors acknowledge the support by the National Research Foundation of Ukraine grant ”Topological phases of matter and excitations in Dirac materials, Josephson junctions and magnets” (No. 2020.02.0051).
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