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| Title: | High-frequency averaging in semi-classical Hartree-type equations |
| Authors: | Giannoulis, Johannes; Mielke, Alexander; Sparber, Christof |
| Issue Date: | 2009 |
| Published in: | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1447, ISSN 0946-8633 |
| Publisher: | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik |
| Abstract: | We investigate the asymptotic behavior of solutions to semi-classical Schröodinger equations with nonlinearities of Hartree type. For a weakly nonlinear scaling, we show the validity of an asymptotic superposition principle for slowly modulated highly oscillatory pulses. The result is based on a high-frequency averaging effect due to the nonlocal nature of the Hartree potential, which inhibits the creation of new resonant waves. In the proof we make use of the framework of Wiener algebras. |
| Keywords: | Nonlinear Schrödinger equation; Hartree-type nonlinearity; Wiener space; propagation of pulses; justification of amplitude equations; high-frequency asymptotics; WKB approximation |
| DDC: | 510 |
| License: | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. |
| Appears in Collections: | Mathematik |
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