@article{oai:repo.qst.go.jp:00077707,
 author = {Pegoraro, Francesco and Bulanov, Sergey and Bulanov, Sergey},
 journal = {PHYSICAL REVIEW D},
 month = {Aug},
 note = {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.},
 title = {Hodograph solutions of the wave equation of nonlinear electrodynamics in the quantum vacuum},
 volume = {100},
 year = {2019}
}