Work

Convergence result for the short pulse equation

Year: 2026

Type: article

Abstract: In this paper, we consider 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. We prove that the solution of a non-local elliptic-hyperbolic system related to the short pulse equation converges to the unique entropy one of the short pulse equation. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the $$L^p$$ L p setting.

Source: Partial Differential Equations and Applications

DOI: 10.1007/s42985-025-00364-9

Authors: Giuseppe Maria Coclite, Lorenzo di Ruvo

Institutions: Polytechnic University of Bari, University of Bari Aldo Moro

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Ministero dell’Istruzione, dell’Università e della Ricerca, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni