On the non-chiral intermediate long wave equation: II. Periodic case

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.
Comment: 27 pages. This is a standalone paper based on Section 6 of arXiv:2005.10781v1