Solving the Characteristic Initial-Value Problem for Colliding Plane Gravitational and Electromagnetic Waves

A method is presented for solving the characteristic initial-value problem for the collision and subsequent nonlinear interaction of plane gravitational or gravitational and electromagnetic waves in a Minkowski background. This method generalizes the monodromy-transform approach to fields with nonanalytic behavior on the characteristics inherent to waves with distinct wave fronts. The crux of the method is in a reformulation of the main nonlinear symmetry reduced field equations as linear integral equations whose solutions are determined by generalized (``dynamical'') monodromy data which evolve from data specified on the initial characteristics (the wave fronts).