Hodograph solutions of the wave equation of nonlinear electrodynamics in the quantum vacuum
Authors: Pegoraro F., Bulanov SV.
Autors Affiliation: Univ Pisa, Enrico Fermi Dept Phys, I-56127 Pisa, Italy; CNR, Natl Inst Opt, Via G Moruzzi 1, I-56124 Pisa, Italy; Inst Phys ASCR, ELI Beamlines Project, Slovance 2, Prague 18221, Czech Republic; Kansai Photon Sci Inst, Natl Inst Quantum & Radiol Sci & Technol QST, 8-1-7 Umemidai, Kizugawa, Kyoto 6190215, Japan; RAS, Prokhorov Gen Phys Inst, Vavilov St 38, Moscow 119991, Russia
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.
Journal/Review: PHYSICAL REVIEW D
Volume: 100 (3) Pages from: 036004 to: 036004
KeyWords: FIELD; COLLISIONS; PHOTONDOI: 10.1103/PhysRevD.100.036004