  We present the foundations of a new solution technique for the characteristic
initial value problem (IVP) of colliding plane gravitational waves. It has
extensive similarities to the approach of Alekseev and Griffiths in 2001, but
we use an inverse scattering method with a Riemann-Hilbert problem (RHP), which
allows for a transformation to a continuous RHP with a solution given in terms
of integral equations for non-singular functions. Ambiguities in this procedure
lead to the construction of a family of spacetimes containing the solution to
the IVP. Therefore the described technique also serves as an interesting
solution generating method. The procedure is exemplified by extending the
Szekeres class of colliding wave spacetimes with 2 additional real parameters.
The obtained solution seems to feature a limiting case of a new type of
impulsive waves, which are circularly polarised.
