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"... This report is preliminary and has not been reviewed for conformity with U.S. Geological Survey editorial standards or with the North American Stratigraphic Code. Any use of trade, firm, or product names is for descriptive purposes only and does not imply ..."

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This report is preliminary and has not been reviewed for conformity with U.S. Geological Survey editorial standards or with the North American Stratigraphic Code. Any use of trade, firm, or product names is for descriptive purposes only and does not imply

### NONLINEAR SCHRÖDINGER EQUATION AND FREQUENCY SATURATION

, 2012

"... We propose an approach that permits to avoid instability phenomena for the nonlinear Schrödinger equations. We show that by approximating the solution in a suitable way, relying on a frequency cut-off, global well-posedness is obtained in any Sobolev space with nonnegative regularity. The error bet ..."

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We propose an approach that permits to avoid instability phenomena for the nonlinear Schrödinger equations. We show that by approximating the solution in a suitable way, relying on a frequency cut-off, global well-posedness is obtained in any Sobolev space with nonnegative regularity. The error between the exact solution and its approximation can be measured according to the regularity of the exact solution, with different accuracy according to the cases considered.

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"... High frequency wave packets for the Schrödinger equation and its numerical approximations Paquets d’ondes a ̀ haute fréquence pour l’équation de Schrödinger et ses approximations numériques Aurora Marica b, Enrique Zuazua a,b ..."

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High frequency wave packets for the Schrödinger equation and its numerical approximations Paquets d’ondes a ̀ haute fréquence pour l’équation de Schrödinger et ses approximations numériques Aurora Marica b, Enrique Zuazua a,b