WIAS Preprint No. 1447, (2009)

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



Authors

  • Giannoulis, Johannes
  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888
  • Sparber, Christof

2010 Mathematics Subject Classification

  • 35B40 35C20 81Q20

Keywords

  • Nonlinear Schrödinger equation, Hartree-type nonlinearity, Wiener space, propagation of pulses, justification of amplitude equations, high-frequency asymptotics, WKB approximation

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.

Appeared in

  • Asymptot. Anal., 70 (2010) pp. 87--100.

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