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
ISSN
15730530
Abstract
Summary: ``We present new soliton equations related to the $A$-typespin 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 spingeneralizations of the BO equation and the ncILW equation via aspin-pole ansatz where the spin-pole dynamics is governed by the spinCM system in the rational and hyperbolic cases, respectively. We alsopropose physics applications of the new equations, and we introduce aspin generalization of the standard intermediate long-wave equationwhich interpolates between the matrix Korteweg--de Vries equation, theHeisenberg ferromagnet equation, and the spin BO equation.''