Hodograph solutions of the wave equation of nonlinear electrodynamics in the quantum vacuum

Year: 2019

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.


Volume: 100 (3)      Pages from: 036004-1  to: 036004-15

More Information: We thank Drs. G. Korn and N. N. Rosanov for fruitful discussions. Supported by the project High Field Initiative (CZ.02.1.01/0.0/0.0/15_003/0000449) from European Regional Development Fund. F. P. thanks the ELI-Beamlines project for its hospitality in September 2018.
DOI: 10.1103/PhysRevD.100.036004

Citations: 7
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