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Jumps, cusps and fractals in the solution of the periodic linear Benjamin-Ono equation
Lyonell Boulton, Breagh Macpherson, Beatrice Pelloni
We establish two complementary results about the regularity of the solution of the periodic initial value problem for the linear Benjamin-Ono equation. We first give a new simple p…
Jumps and cusps: a new revival effect in local dispersive PDEs
Lyonell Boulton, George Farmakis, Beatrice Pelloni +1
We study the presence of a non-trivial revival effect in the solution of linear dispersive boundary value problems for two benchmark models which arise in applications: the Airy eq…
Revivals, or the Talbot effect, for the Airy equation
Beatrice Pelloni, David A. Smith
We study Dirichlet-type problems for the simplest third-order linear dispersive PDE, often referred to as the Airy equation. Such problems have not been extensively studied, perhap…