## Dispersive decay for the 1D Klein-Gordon equation with variable coefficient nonlinearities

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- by Jacob Sterbenz PDF
- Trans. Amer. Math. Soc.
**368**(2016), 2081-2113 Request permission

## Abstract:

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 $L^\infty$ 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.## References

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## Additional Information

**Jacob Sterbenz**- Affiliation: Department of Mathematics, University of California San Diego, La Jolla, California 92093-0112
- MR Author ID: 733516
- Email: jsterbenz@math.ucsd.edu
- Received by editor(s): July 31, 2013
- Received by editor(s) in revised form: September 1, 2013, April 28, 2014, and May 22, 2014
- Published electronically: May 6, 2015
- Additional Notes: The author was supported in part by NSF grant DMS-1001675.
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**368**(2016), 2081-2113 - MSC (2010): Primary 35L70
- DOI: https://doi.org/10.1090/tran/6478
- MathSciNet review: 3449234