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).