On persistence properties in weighted spaces for solutions of the fractional Korteweg–de Vries equation

Abstract

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.