论文标题
具有自洽潜力和相关Yajima-oikawa类型方程的可集成的普遍的海森贝格·弗罗格纳特方程
Integrable generalized Heisenberg ferromagnet equations with self-consistent potentials and related Yajima-Oikawa type equations
论文作者
论文摘要
我们考虑一些描述长（LS）波的相互作用的非线性模型。此类LS模型是通过各种动机得出和提出的，这些动机主要来自流体和血浆物理学。在本文中，我们研究了一些可集成的LS模型，即Yajima-oikawa方程，Newell方程，MA方程，GenG-LI方程式等。特别是，发现了这些集成LS模型（方程）的量规等效物。实际上，LS方程的这些量规等值是具有自稳态电位（HFESCP）的可整合的Heisenberg Ferromagnet方程（HFE）。给出了这些HFESCP的相关LAX表示。我们还提出了几个自旋方程，它们描述了铁磁材料中自旋和晶格子系统的非线性相互作用。
We consider some nonlinear models describing interactions of long and short (LS) waves. Such LS models have been derived and proposed with various motivations, which mainly come from fluid and plasma physics. In this paper, we study some of integrable LS models, namely, the Yajima-Oikawa equation, the Newell equation, the Ma equation, the Geng-Li equation and etc. In particular, the gauge equivalent counterparts of these integrable LS models (equations) are found. In fact, these gauge equivalents of the LS equations are integrable generalized Heisenberg ferromagnet equations (HFE) with self-consistent potentials (HFESCP). The associated Lax representations of these HFESCP are given. We also presented several spin-phonon equations which describe nonlinear interactions of spin and lattice subsystems in ferromagnetic materials.
