  The process of photon-photon scattering in vacuum is investigated
analytically in the long-wavelength limit within the framework of the
Euler-Heisenberg Lagrangian. In order to solve the nonlinear partial
differential equations (PDEs) obtained from this Lagrangian use is made of the
hodograph transformation. This transformation makes it possible to turn a
system of quasilinear PDEs into a system of linear PDEs. Exact solutions of the
equations describing the nonlinear interaction of electromagnetic waves in
vacuum in a one-dimensional configuration are obtained and analyzed.
