Asymptotic behavior in time of solutions to complex-valued nonlinear Klein-Gordon equation in one space dimension

Abstract

We consider the long time behavior of solutions to the initial value problem for the ``complex-valued cubic nonlinear Klein-Gordon equation (NLKG) in one space dimension. In [12], Sunagawa derived the $L^{\\infty}$ decay estimate of solutions to (NLKG). In this note, we obtain the large time asymptotic profile of solutions to (NLKG).