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arXiv · 1612.00109

Modified scattering for the quadratic nonlinear Klein-Gordon equation in two dimensions

Satoshi Masaki·Jun-ichi Segata
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Abstract

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.

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Satoshi Masaki, Jun-ichi Segata. 2016-12-01. Modified scattering for the quadratic nonlinear Klein-Gordon equation in two dimensions. https://arxiv.org/abs/1612.00109

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