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

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.

16 pages

References in corpus (2)

• Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg-de Vries equation
• Long range scattering for nonlinear Schrödinger equations with critical homogeneous nonlinearity

Cited by in corpus (1)

• Modified scattering for the Klein-Gordon equation with the critical nonlinearity in three dimensions