Spin generalizations of the Benjamin-Ono equation

TL;DR

This paper introduces new spin generalizations of the Benjamin-Ono and ncILW equations, providing multi-soliton solutions and connecting them to spin Calogero-Moser systems, with potential applications in physics.

Contribution

It presents novel spin generalizations of integrable equations and derives multi-soliton solutions linked to spin Calogero-Moser systems, expanding the understanding of spin-related integrable models.

Findings

Derived multi-soliton solutions for spin BO and ncILW equations

Connected spin pole dynamics to spin Calogero-Moser systems

Proposed a spin intermediate long-wave equation with physical applications

Abstract

We present new soliton equations related to the $A$-type spin Calogero-Moser (CM) systems introduced by Gibbons and Hermsen. These equations are spin generalizations of the Benjamin-Ono (BO) equation and the recently introduced non-chiral intermediate long-wave (ncILW) equation. We obtain multi-soliton solutions of these spin generalizations of the BO equation and the ncILW equation via a spin-pole ansatz where the spin-pole dynamics is governed by the spin CM system in the rational and hyperbolic cases, respectively. We also propose physics applications of the new equations, and we introduce a spin generalization of the standard intermediate long-wave equation which interpolates between the matrix Korteweg-de Vries equation, the Heisenberg ferromagnet equation, and the spin BO equation.