High-frequency averaging in semi-classical Hartree-type equations
Analysis of PDEs
2018-01-17 v2
Abstract
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.
Cite
@article{arxiv.0909.5640,
title = {High-frequency averaging in semi-classical Hartree-type equations},
author = {Johannes Giannoulis and Alexander Mielke and Christof Sparber},
journal= {arXiv preprint arXiv:0909.5640},
year = {2018}
}
Comments
13 pages; Version 2: Added Remark 2.2