Elliptic soliton solutions of the spin non-chiral intermediate long-wave equation

TL;DR

This paper constructs elliptic multi-soliton solutions for the spin non-chiral intermediate long-wave equation using a spin-pole ansatz linked to the elliptic spin Calogero-Moser system, including a dynamical background.

Contribution

It introduces a novel spin-pole ansatz with a dynamical background for the sncILW equation and establishes its solutions via a Bäcklund transformation for the elliptic sCM system.

Findings

Constructed elliptic multi-soliton solutions for the sncILW equation.

Linked solutions to the elliptic sCM system with specific initial conditions.

Extended solutions to the spin Benjamin-Ono equation with non-trivial backgrounds.

Abstract

We construct elliptic multi-soliton solutions of the spin non-chiral intermediate long-wave (sncILW) equation with periodic boundary conditions. These solutions are obtained by a spin-pole ansatz including a dynamical background term; we show that this ansatz solves the periodic sncILW equation provided the spins and poles satisfy the elliptic $A$-type spin Calogero-Moser (sCM) system with certain constraints on the initial conditions. The key to this result is a B\"{a}cklund transformation for the elliptic sCM system which includes a non-trivial dynamical background term. We also present solutions of the sncILW equation on the real line and of the spin Benjamin-Ono equation which generalize previously obtained solutions by allowing for a non-trivial background term.