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Cusp Revivals and Fractal Regularity of the Linear Benjamin-Ono Equation

A regularity study of the periodic linear Benjamin-Ono equation showing two complementary behaviours of its solution: at a dense set of rational times, jump discontinuities in the initial data reappear as logarithmic cusp singularities (cusp revivals), proved by relating the equation to the linear Schrodinger (Talbot) problem; and for bounded-variation initial data, at almost every irrational time the solution graph is continuous but fractal, with upper Minkowski dimension 3/2.