Benjamin-Ono方程的自旋推广
Spin generalizations of the Benjamin-Ono equation
摘要：
本文提出了与Gibbons和Hermsen提出的$A$型自旋Calogero-Moser（CM）系统有关的新孤子方程.这些方程是Benjamin-Ono（BO）方程和最近引入的非手征中间长波（ncILW）方程的自旋推广。我们通过自旋-磁极分析得到了BO方程和ncILW方程的自旋推广的多孤子解，其中自旋-磁极动力学分别由自旋CM系统在有理和双曲情形下控制.我们还提出了新方程的物理应用，我们介绍了一个自旋推广的标准中间长波方程之间的矩阵Korteweg-de Vries方程，海森堡铁磁体方程，和自旋BO方程。
英文摘要：
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.
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