Dynamics of a string and a zero-string in the field of gravitational waves

It is shown that weak gravitational waves, under the appropriate choice of initial data, do not practically influence a movement of a closed zero-string. But in the Peres space-time, which traditionally describes a 'strong' gravitational field, a closed zero-string oscillated in the plane yz, periodically shrinking into a point, and simulancously moves along the axis x