Spin generalizations of the Benjamin-Ono equation

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.

34 pages

References in corpus (6)

• Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
• Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids
• Integrable hydrodynamics of Calogero-Sutherland model: Bidirectional Benjamin-Ono equation
• On the non-chiral intermediate long wave equation II: periodic case
• The non-chiral intermediate Heisenberg ferromagnet equation
• Integrability, conservation laws and solitons of a many-body dynamical system associated with the half-wave maps equation

Cited by in corpus (4)

• An explicit formula for the Benjamin--Ono equation
• Elliptic soliton solutions of the spin non-chiral intermediate long-wave equation
• Consistency of the Bäcklund transformation for the spin Calogero-Moser system
• Periodic solutions of the non-chiral intermediate Heisenberg ferromagnet equation described by elliptic spin Calogero-Moser dynamics