Scattering in the nonlinear Lamb system

We obtain long time asymptotics for the solutions to a string coupled to a nonlinear oscillator: each finite energy solution decays to a sum of a stationary state and a dispersive wave. The asymptotics hold in global energy norm. The dispersive waves are expressed via initial data and solution to an...

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Bibliographic Details
Published in:Physics letters. A 2009-03, Vol.373 (11), p.1005-1010
Main Authors: Komech, A.I., Merzon, A.E.
Format: Article
Language:English
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Summary:We obtain long time asymptotics for the solutions to a string coupled to a nonlinear oscillator: each finite energy solution decays to a sum of a stationary state and a dispersive wave. The asymptotics hold in global energy norm. The dispersive waves are expressed via initial data and solution to an ordinary differential equation. The asymptotics give a mathematical model for the Bohr's transitions between quantum stationary states.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2009.01.054