  In terms of gravitational solitons, we study gravitational non-linear effects
of gravitational solitary waves such as Faraday rotation. Applying the
Pomeransky's procedure for inverse scattering method, which has been recently
used for constructing stationary black hole solutions in five dimensions to a
cylindrical spacetime in four dimensions, we construct a new cylindrically
symmetric soliton solution. This is the first example to be applied to the
cylindrically symmetric case. In particular, we clarify the difference from the
Tomimatsu's single soliton solution, which was constructed by the
Belinsky-Zakharov's procedure.
