title: Paraxial envelope X waves.
abstract: Localized, stationary, X-type solutions of the paraxial wave equation are described. Unlike conventional X waves, these are luminal, envelope X waves sustained by a material medium because of the interplay of dispersion and diffraction.
authors.affiliation: Departamento de Física Aplicada, Escuela de Ingenieros de Madrid, Universidad Politècnica de Madrid, Rios Rosas 21, 28003 Madrid, Spain. porras@dfarn.upm.es
authors.forename: Miguel A
authors.initials: MA
authors.lastname: Porras
authors.forename: Stefano
authors.initials: S
authors.lastname: Trillo
authors.forename: Claudio
authors.initials: C
authors.lastname: Conti
authors.forename: Paolo
authors.initials: P
authors.lastname: Di Trapani