Asymptotic Solutions of Two-Dimensional Hartree-Type Equations Localized in the Neighborhood of Line Segments

被引：0
|
作者：
A. V. Pereskokov
机构：
[1] Moscow Power Engineering Institute (Technical University),
来源：
Theoretical and Mathematical Physics | 2002年 / 131卷
关键词：
semiclassical asymptotic solutions; quantization rule; Hartree equation; Airy polaron;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider the eigenvalue problem for the two-dimensional Schrödinger equation containing an integral Hartree-type nonlinearity with an interaction potential having a logarithmic singularity. Global asymptotic solutions localized in the neighborhood of a line segment in the plane are constructed using the matching method for asymptotic expansions. The Bogoliubov and Airy polarons are used as model functions in these solutions. An analogue of the Bohr–Sommerfeld quantization rule is established to find the related series of eigenvalues.
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页码：775 / 790
页数：15
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