On the spectrum of the periodic focusing Zakharov–Shabat operator
On the spectrum of the periodic focusing Zakharov–Shabat operator
复制标题
DOI：
10.4171/jst/432
复制
发表时间：
2020-10
影响因子：
1
通讯作者：
G. Biondini;Jeffrey Oregero;A. Tovbis
中科院分区：
文献类型：
--
作者：
G. Biondini;Jeffrey Oregero;A. Tovbis
研究了圆上聚焦 Zakharov-Shabat 算子的谱，并考虑了其对半经典参数存在的显式依赖性。获得了一些新结果。特别是：（i）证明了解析集由两个连通分量组成，（ii）获得了 Floquet 和 Dirichlet 谱位置的新界限，其中一些明确取决于半经典参数的值，（iii）证明了谱在半经典极限下定位于谱平面中的“十字”。通过讨论几个分析或数值计算光谱的例子来说明结果。
The spectrum of the focusing Zakharov-Shabat operator on the circle is studied, and its explicit dependence on the presence of a semiclassical parameter is also considered. Several new results are obtained. In particular: (i) it is proved that the resolvent set is comprised of two connected components, (ii) new bounds on the location of the Floquet and Dirichlet spectra are obtained, some of which depend explicitly on the value of the semiclassical parameter, (iii) it is proved that the spectrum localizes to a"cross"in the spectral plane in the semiclassical limit. The results are illustrated by discussing several examples in which the spectrum is computed analytically or numerically.