论文标题
在定期聚焦Zakharov-Shabat操作员的范围内
On the spectrum of the periodic focusing Zakharov-Shabat operator
论文作者
论文摘要
研究了圆圈上聚焦Zakharov-Shabat操作员的光谱，并考虑了其对半经典参数的存在的明确依赖性。获得了几个新结果。 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.通过讨论几个示例，在分析或数字上计算频谱的几个示例来说明结果。
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.
