  The initial-value problem for cylindrical gravitational waves is studied
through the development of the inverse scattering method scheme. The inverse
scattering transform in this case can be viewed as a transformation of the
Cauchy data to the data on the symmetry axis. Riemann-Hilbert problem, which
serves as inverse transformation, is formulated in two different ways. We
consider Einstein-Rosen waves to illustrate the method.
