Hodograph solutions of the wave equation of nonlinear electrodynamics in the quantum vacuum
arXiv:1903.01733 · doi:10.1103/PhysRevD.100.036004
Abstract
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.
17 pages
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- Generation of High Order Harmonics in Heisenberg-Euler Electrodynamics
- Nonlinear electrodynamics at cylindrical "cumulation" fronts