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On dispersion of small energy solutions of the nonlinear Klein Gordon equation with a potential
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 133, Number 5, October 2011
- pp. 1421-1468
- 10.1353/ajm.2011.0034
- Article
- Additional Information
In this paper we study small amplitude solutions of nonlinear Klein Gordon equations
with a potential. Under suitable smoothness and decay assumptions on the potential and
a genericity assumption on the nonlinearity, we prove that all small energy solutions
are asymptotically free. In cases where the linear system has at most one bound state
the result was already proved by Soffer and Weinstein: we obtain here a result valid in
the case of an arbitrary number of possibly degenerate bound states. The proof is based
on a combination of Birkhoff normal form techniques and dispersive estimates.