(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Giannoulis, Johannes; Mielke, Alexander; Sparber, Christof
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.
