  We introduce a scheme of a photonic coupler built of two parallel
topological-insulator slab waveguides with the intrinsic Kerr nonlinearity,
separated by a gap. Josephson oscillations (JO) of a single edge soliton
created in one slab, and of a pair of solitons created in two slabs, are
considered. The single soliton jumping between the slabs is subject to quick
radiative decay. On the other hand, the JO of the copropagating soliton pair
may be essentially more robust, as one soliton can absorb dispersive waves
emitted by the other. The most robust JO regime is featured by the pair of
solitons with phase shift $\pi$ between them.
