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New cylindrical gravitational soliton waves and gravitational Faraday rotation

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.