Nonlinear Schrödinger equations and simple Lie algebras
Nonlinear Schrödinger equations and simple Lie algebras
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DOI：
10.1007/bf01214664
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发表时间：
1983-09
影响因子：
2.4
通讯作者：
A. Fordy;P. P. Kulish-P.
中科院分区：
文献类型：
--
作者：
A. Fordy;P. P. Kulish-P.
我们将一个可积的广义非线性薛定谔(NLS)方程组与每个厄米特对称空间联系起来。这些NLS方程被认为是更一般系统的约化，这一次与约化的齐次空间有关。非线性项与适当几何空间的曲率张量和扭转张量有关。用“r-矩阵”技术研究了哈密顿结构，并证明了所有这些方程都是“正则”的。在整个约化过程中，这种哈密顿结构不会退化。上述方程组中的每一个都是规范等价的广义铁磁体。根据相应的NLS型方程讨论了后者的约化。
We associate a system of integrable, generalised nonlinear Schrödinger (NLS) equations with each Hermitian symmetric space. These NLS equations are considered as reductions of more general systems, this time associated with a reductive homogeneous space. The nonlinear terms are related to the curvature and torsion tensors of the appropriate geometrical space. The Hamiltonian structure is investigated using “r-matrix” techniques and shown to be “canonical” for all these equations. Throughout the reduction procedure this Hamiltonian structure does not degenerate. Each of the above systems of equations is gauge equivalent to a generalised ferromagnet. Reductions of the latter are discussed in terms of the corresponding NLS type equations.