학술논문
Spin generalizations of the Benjamin-Ono equation.
Document Type
Journal
Author
Berntson, Bjorn K. (S-RIT-DP) AMS Author Profile; Langmann, Edwin (S-RIT-DP) AMS Author Profile; Lenells, Jonatan (S-RIT) AMS Author Profile
Source
Subject
37 Dynamical systems and ergodic theory -- 37K Infinite-dimensional Hamiltonian systems
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
37K10
Language
English
Abstract
Summary: ``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.''