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MODIFIED SCATTERING FOR THE QUADRATIC NONLINEAR KLEIN-GORDON EQUATION IN TWO DIMENSIONS.
- Source :
-
Transactions of the American Mathematical Society . Nov2018, Vol. 370 Issue 11, p8155-8170. 16p. - Publication Year :
- 2018
-
Abstract
- In this paper, we consider the long time behavior of the solution to the quadratic nonlinear Klein-Gordon equation (NLKG) in two space dimensions: ( + 1)u = λ|u|u, t ∈ R, x ∈ R2, where = ∂t² - Δ is d'Alembertian. For a given asymptotic profile uap, we construct a solution u to (NLKG) which converges to uap as t → ∞. Here the asymptotic profile uap is given by the leading term of the solution to the linear Klein-Gordon equation with a logarithmic phase correction. Construction of a suitable approximate solution is based on Fourier series expansion of the nonlinearity. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 370
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 131723588
- Full Text :
- https://doi.org/10.1090/tran/7262