Journal
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 368, Issue 3, Pages 2081-2113Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/tran/6478
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Funding
- NSF [DMS-1001675]
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We study the 1D Klein-Gordon equation with variable coefficient nonlinearity. This problem exhibits an interesting resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the solutions. In the case when only the cubic coefficients are variable we prove L-infinity scattering and smoothness of the solution in weighted spaces with the help of both quadratic and cubic normal forms transformations. In the case of cubic interactions these normal forms appear to be novel.
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