  We study integrability properties of the non-chiral intermediate long wave
(ncILW) equation with periodic boundary conditions. The ncILW equation was
recently introduced by the authors as a parity-invariant relative of the
intermediate long wave equation. For this new equation we: (a) derive a Lax
pair, (b) derive a Hirota bilinear form, (c) use the Hirota method to construct
the periodic multi-soliton solutions, (d) derive a B\"{a}cklund transformation,
(e) use the B\"{a}cklund transformation to obtain an infinite number of
conservation laws.
