High-frequency averaging in semi-classical Hartree-type equations

Details High-frequency averaging in semi-classical Hartree-type equations High-frequency averaging in semi-classical Hartree-type equations

2009-09-30

arxiv.org/abs/0909.5640v2

Mathematics

Analysis of PDEs

13 pages; Version 2: Added Remark 2.2

Scientific paper

We investigate the asymptotic behavior of solutions to semi-classical Schroedinger 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.

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