Eur. Phys. J. D 21, 217-228 (2002)
https://doi.org/10.1140/epjd/e2002-00198-7

New localized Superluminal solutions to the wave equations with finite total energies and arbitrary frequencies^*

¹ DMO–FEEC, State University of Campinas, Campinas S.P., Brazil
² Facoltà di Ingegneria, Università statale di Bergamo, Dalmine (BG), Italy
³ INFN—Sezione di Milano, Milan, Italy
⁴ C.C.S., State University of Campinas, Campinas S.P., Brazil

Corresponding author: ^a recami@mi.infn.it

Received: 23 June 2002
Published online: 24 September 2002

Abstract

By a generalized bidirectional decomposition method, we obtain new Superluminal localized solutions to the wave equation (for the electromagnetic case, in particular) which are suitable for arbitrary frequency bands; several of them being endowed with finite total energy. We construct, among the others, an infinite family of generalizations of the so-called “X-shaped" waves. Results of this kind may find application in the other fields in which an essential role is played by a wave-equation (like acoustics, seismology, geophysics, gravitation, elementary particle physics, etc.).