2020/11/30 by Oscar Riaño
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Burgers' equation #Classical mechanics #Continuation #Dispersive partial differential equation #Inviscid flow #Korteweg–de Vries equation #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Partial differential equation #Persistence (discontinuity) #Perturbation (astronomy) #Physics #Polynomial #Thermodynamics #Work (physics) #math.AP #msc:35B05 #msc:35B60 #msc:35Q53
paper · pdf · doi:10.1088/1361-6544/abf5bd
52 pages, Updated introduction
openalex created_date 2020/11/23 · arxiv created 2021/04/15 · openalex publication_date 2021/06/21 · arxiv updated 2021/08/11 · openalex updated_date 2026/08/05
Abstract Persistence problems in weighted spaces have been studied for different dispersive models involving non-local operators. Generally, these models do not propagate polynomial weights of arbitrary magnitude, and the maximum decay rate is associated with the dispersive part of the equation. Altogether, this analysis is complemented by unique continuation principles that determine optimal spatial decay. This work is intended to establish the above questions for a weakly dispersive perturbation of the inviscid Burgers equation. More precisely, we consider the fractional Korteweg–de Vries equation, which comprises the Burgers–Hilbert equation and dispersive effects weaker than those of the Benjamin–Ono equation.