Geometric optics and instability for semi-classical Schrodinger equations

Details Geometric optics and instability for semi-classical Schrodinger equations Geometric optics and instability for semi-classical Schrodinger equations

2005-05-23

arxiv.org/abs/math/0505468v4

Arch. Ration. Mech. Anal. 183 (2007), no. 3, 525-553.

Mathematics

Analysis of PDEs

22 pages. Corollary 1.7 added

Scientific paper

10.1007/s00205-006-0017-5

We prove some instability phenomena for semi-classical (linear or) nonlinear Schrodinger equations. For some perturbations of the data, we show that for very small times, we can neglect the Laplacian, and the mechanism is the same as for the corresponding ordinary differential equation. Our approach allows smaller perturbations of the data, where the instability occurs for times such that the problem cannot be reduced to the study of an o.d.e.

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