  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.
