论文标题
具有衰减潜力的非自我支持狄拉克操作员的半经典WKB问题
Semiclassical WKB problem for the non-self-adjoint Dirac operator with a decaying potential
论文作者
论文摘要
在本文中，我们研究了非自发狄拉克运算符的散射数据的半经典行为，其无穷大时具有相当平滑但不一定是分析势衰减的。特别是，使用回到Langer和Olver的思想和方法，我们为零件（略微）从零开始（略微）提供了完全严格的均匀均匀的半经典分析，并为特征值位置的均匀Bohr-Sommerfeld条件提供了严格的证明。鉴于扎卡罗夫（Zakharov）和沙巴特（Shabat）发现的众所周知的事实，我们的分析是由对聚焦立方NLS方程的潜在应用激发的，认为狄拉克操作员的光谱分析是通过逆散射理论解决NLS方程的基础。本文补充并扩展了富士和第二作者的先前作品，该作者认为这是一个严格的分析潜力的更受限制的问题。
In this paper we examine the semiclassical behaviour of the scattering data of a non-self-adjoint Dirac operator with a fairly smooth but not necessarily analytic potential decaying at infinity. In particular, using ideas and methods going back to Langer and Olver, we provide the complete rigorous uniform semiclassical analysis of the scattering coefficients away (slightly) from zero, and the rigorous proof of the uniform Bohr-Sommerfeld condition for the location of the eigenvalues. Our analysis is motivated by the potential applications to the focusing cubic NLS equation, in view of the well-known fact discovered by Zakharov and Shabat that the spectral analysis of the Dirac operator is the basis of the solution of the NLS equation via inverse scattering theory. This paper complements and extends a previous work of Fujiié and the second author, which considered a more restricted problem for a strictly analytic potential.
