On the non-chiral intermediate long wave equation: II. Periodic case. (4th August 2022) - Berntson, Bjorn K; Langmann, Edwin; Lenells, Jonatan
Abstract: 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 a family of exact periodic wave solutions, (d) derive a Bäcklund transformation, (e) use the Bäcklund transformation to obtain an infinite number of conservation laws.