Remarks on the asymptotic behavior of the cubic nonlinear Klein-Gordon equations in one space dimension

Abstract

We study the large time behavior of the solution to the Cauchy problem for the one-dimensional, cubic nonlinear Klein-Grodon equation with complex-valued initial data. We show that the small amplitude solution decays like $t^{-1/2}$ as $t$ tends to infinity. Several remarks are also given on the large time asymptotics.