On the non-chiral intermediate long wave equation

We study integrability properties of the non-chiral intermediate long wave equation recently introduced by the authors as a parity-invariant variant of the intermediate long wave equation. For this new equation we: (a) derive a Lax pair, (b) derive a Hirota bilinear form, (c) derive a Backlund transformation, (d) use, separately, the Backlund transformation and the Lax representation to obtain an infinite number of conservation laws. In the last section, we extend our results to the elliptic integrable system obtained by imposing periodic boundary conditions on the non-chiral intermediate long wave equation.