WKB analysis for nonlinear Schr\"{o}dinger equations with potential
偏微分方程分析
2016-08-16 v2 数学物理
math.MP
摘要
We justify the WKB analysis for the semiclassical nonlinear Schr\"{o}dinger equation with a subquadratic potential. This concerns subcritical, critical, and supercritical cases as far as the geometrical optics method is concerned. In the supercritical case, this extends a previous result by E. Grenier; we also have to restrict to nonlinearities which are defocusing and cubic at the origin, but besides subquadratic potentials, we consider initial phases which may be unbounded. For this, we construct solutions for some compressible Euler equations with unbounded source term and unbounded initial velocity.
引用
@article{arxiv.math/0601611,
title = {WKB analysis for nonlinear Schr\"{o}dinger equations with potential},
author = {Rémi Carles},
journal= {arXiv preprint arXiv:math/0601611},
year = {2016}
}
备注
25 pages, 11pt, a4. Appendix withdrawn, due to some inconsistencies