On asymptotic completeness of scattering in the nonlinear Lamb system, II

We establish the asymptotic completeness in the nonlinear Lamb system for hyperbolic stationary states. For the proof we construct a trajectory of a reduced equation (which is a nonlinear nonautonomous ordinary differential equation) converging to a hyperbolic stationary point using the inverse func...

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Bibliographic Details
Published in:Journal of mathematical physics 2013-01, Vol.54 (1), p.1
Main Authors: Komech, A. I., Merzon, A. E.
Format: Article
Language:English
Subjects:
Asymptotic methods
Asymptotic properties
Banach spaces
Completeness
Convergence
Differential equations
Inverse
Lamb
Mathematical analysis
Nonlinearity
Ordinary differential equations
Proof theory
Trajectories
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Summary:We establish the asymptotic completeness in the nonlinear Lamb system for hyperbolic stationary states. For the proof we construct a trajectory of a reduced equation (which is a nonlinear nonautonomous ordinary differential equation) converging to a hyperbolic stationary point using the inverse function theorem in a Banach space. We give counterexamples which show nonexistence of such trajectories for nonhyperbolic stationary points.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4773288