Semiclassical Singularity Propagation Property for Schr\"odinger Equations

Shu Nakamura

Semiclassical Singularity Propagation Property for Schr\"odinger Equations

偏微分方程分析 2007-09-18 v2 数学物理 math.MP

作者: Shu Nakamura

摘要

We consider Schr\"odinger equations with variable coefficients, and it is supposed to be a long-range type perturbation of the flat Laplacian on $R^n$ . We characterize the wave front set of solutions to Schr\"odinger equations in terms of the initial state. Then it is shown that the singularity propagates following the classical flow, and it is formulated in a semiclassical settings. Methods analogous to the long-range scattering theory, in particular a modified free propagator, are employed.

关键词

schrödinger equation nonlinear schrödinger equation scattering theory

引用

@article{arxiv.math/0605742,
  title  = {Semiclassical Singularity Propagation Property for Schr\"odinger Equations},
  author = {Shu Nakamura},
  journal= {arXiv preprint arXiv:math/0605742},
  year   = {2007}
}

备注

29 pages

相关论文

查看更多相关论文 →