Large time asymptotics of solutions to nonlinear Klein-Gordon systems

Abstract

Consider a nonlinear system of two Klein-Gordon equations with masses $m$ and $\mu$. We construct a solution whose amplitude is modulated by the nonlinear interaction when $\mu = m$ or $\mu = 3m$, whereas, when $\mu \ne m$ and $\mu \ne 3m$, the influence of the nonlinearity is negligible and the solution behaves like a free solution as $t \to \infty$.