Geometric optics and instability for semi-classical Schrödinger equations - Archive ouverte HAL
Article Dans Une Revue Archive for Rational Mechanics and Analysis Année : 2007

Geometric optics and instability for semi-classical Schrödinger equations

Résumé

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.

Dates et versions

hal-00004971 , version 1 (26-09-2005)

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Rémi Carles. Geometric optics and instability for semi-classical Schrödinger equations. Archive for Rational Mechanics and Analysis, 2007, 183 (3), pp.525-553. ⟨10.1007/s00205-006-0017-5⟩. ⟨hal-00004971⟩

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