A non-local elliptic–hyperbolic system related to the short pulse equation. (January 2020)

• Record Type: Journal Article
• Authors: Coclite, Giuseppe Maria; di Ruvo, Lorenzo
• Is Part Of: Nonlinear analysis. Volume 190(2020)
• Publication Date: 2020-01
• Subjects: 35G25 -- 35K55; Existence -- Uniqueness -- Stability -- Short pulse equation -- Non-local formulation -- Cauchy problem; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111606
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we prove the well-posedness of a non-local elliptic–hyperbolic system related to the short pulse equation. It is a model which describes the evolution of the electrical field of linearly polarized continuum spectrum pulses in optical waveguides, including fused-silica telecommunication-type or photonic-crystal fibers, as well as hollow capillaries filled with transparent gases.