Nonlinear wave and Schrödinger equations. I: Instability of periodic and quasiperiodic solutions
type: Item
instance of: scholarly article
title: Nonlinear wave and Schrödinger equations. I: Instability of periodic and quasiperiodic solutions
zbMATH Open document ID: 0780.35106
DOI: 10.1007/BF02096645
published in: Communications in Mathematical Physics
publication date: 1993-06-29T00:00:00Z
review text: Stability of periodic and quasiperiodic solutions of linear wave and Schrödinger equations under nonlinear perturbations is investigated. Using the Mourre estimate and the Fermi Golden rule for non-elliptic and nonlinear equations the author shows that for the wave equation such solutions are unstable for generic perturbations and gives spectral conditions which guarantee instability. In this case of the Schrödinger equation periodic solutions are stable while quasiperiodic ones are not. These results are extended to periodic solutions of nonlinear equations. Some illustrative examples are considered.
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B10
zbMATH DE Number: 221163
zbMATH Keywords: nonlinear wave equations
zbMATH Keywords: stability
zbMATH Keywords: quasiperiodic solutions
zbMATH Keywords: Mourre estimate
zbMATH Keywords: Fermi Golden rule
zbMATH Keywords: spectral conditions
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: periodic solutions
author: I. M. Sigal
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 221163