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

TL;DR

This paper investigates the integrability of the non-chiral intermediate long wave equation with periodic boundary conditions, deriving key structures like Lax pairs, soliton solutions, and conservation laws to establish its integrability.

Contribution

The authors introduce the non-chiral ILW equation with periodic boundary conditions and derive its Lax pair, Hirota form, multi-soliton solutions, Bäcklund transformation, and conservation laws, advancing understanding of its integrability.

Findings

Derived a Lax pair for the ncILW equation

Constructed periodic multi-soliton solutions

Established an infinite number of conservation laws

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 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.