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

摘要

We consider the long time behavior of solutions to the initial value prob-lem for the "complex-valued" cubic nonlinear Klein-Gordon equation (NLKG) in one space dimension. In [12], Sunagawa derived the L-infinity decay estimate of solutions to (NLKG). In this note, we obtain the large time asymptotic profile of solutions to (NLKG).