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 behaviour on the characteristics inherent to waves with
distinct wave fronts. The cruxof 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 wavefronts).
This is a pre-print. The definitive version: GRIFFITHS, G.A. and ALEKSEEV, J.B., 2002. Solving the characteristic initial-value problem for colliding plane gravitational and electromagnetic waves. Physical Review, 87(22), Art. No. 221101, at: http://prl.aps.org/.