Rotating cosmic strings and gravitational soliton waves

Using the Belinsky-Zakharov inverse scattering method, a four-parameter family of cylindrically symmetric solutions of Einstein's vacuum equations is obtained. They are of Petrov type D and, for a certain range of the parameters, represent solitonlike gravitational waves interacting with a straight-line cosmic string. Their interpretation as rotating cosmic strings occupying the axis of symmetry is also investigated