Modified scattering for the quadratic nonlinear Klein–Gordon equation in two dimensions
| Autor: | Satoshi Masaki, Jun Ichi Segata |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Logarithm
Applied Mathematics General Mathematics 010102 general mathematics Mathematical analysis Gauge (firearms) Space (mathematics) 01 natural sciences 010101 applied mathematics Nonlinear system symbols.namesake Quadratic equation symbols 0101 mathematics Invariant (mathematics) Klein–Gordon equation Fourier series Mathematics |
| Zdroj: | Transactions of the American Mathematical Society. 370:8155-8170 |
| ISSN: | 1088-6850 0002-9947 |
| DOI: | 10.1090/tran/7262 |
| Popis: | In this paper, we consider the long time behavior of solution to the quadratic gauge invariant nonlinear Klein-Gordon equation (NLKG) in two space dimensions. For a given asymptotic profile, we construct a solution to (NLKG) which converges to given asymptotic profile as t goes infinity. Here the asymptotic profile 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. |
| Databáze: | OpenAIRE |
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