  Using a cylindrical soliton solution to the four-dimensional vacuum Einstein
equation, we study non-linear effects of gravitational waves such as Faraday
rotation and time shift phenomenon. In the previous work, we analyzed the
single-soliton solution constructed by the Pomeransky's improved inverse
scattering method. In this work, we construct a new two-soliton solution with
complex conjugate poles, by which we can avoid light-cone singularities
unavoidable in a single soliton case. In particular, we compute amplitudes of
such non-linear gravitational waves and time-dependence of the polarizations.
Furthermore, we consider the time shift phenomenon for soliton waves, which
means that a wave packet can propagate at slower velocity than light.
