Ricerche di Matematica

, Volume 68, Issue 2, pp 341–357 | Cite as

Travelling waves and light-front approach in relativistic electrodynamics

  • Gaetano FioreEmail author
  • Paolo Catelan


We briefly report on a recent proposal (Fiore in J Phys A Math Theor 51:085203, 2018) for simplifying the equations of motion of charged particles in an electromagnetic field \(F^{\mu \nu }\) that is the sum of a plane travelling wave \(F_t^{\mu \nu }(ct\!-\!z)\) and a static part \(F_s^{\mu \nu }(x,y,z)\); it adopts the light-like coordinate \(\xi =ct\!-\!z\) instead of time t as an independent variable. We illustrate it in a few cases of extreme acceleration, first of an isolated particle, then of electrons in a plasma in plane hydrodynamic conditions: the Lorentz–Maxwell and continuity PDEs can be simplified or sometimes even completely reduced to a family of decoupled systems of ordinary ones; this occurs e.g. with the impact of the travelling wave on a vacuum-plasma interface (what may produce plasma waves or the slingshot effect).


Nonlinear PDEs Laser-driven acceleration Laser-plasma interactions 

Mathematics Subject Classification

35Qxx 76Wxx 82D10 


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Copyright information

© Università degli Studi di Napoli "Federico II" 2018

Authors and Affiliations

  1. 1.Dip. di Matematica e ApplicazioniUniversità di Napoli “Federico II”, Complesso Universitario Monte S. AngeloNaplesItaly
  2. 2.INFN, Sez. di Napoli, Complesso MSANaplesItaly
  3. 3.CEEA, Escuela Superior Politécnica del ChimborazoRiobambaEcuador
  4. 4.Dip. di Matematica ed InformaticaUniversitá della CalabriaArcavacata, RendeItaly

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