The nonlocality of the Pavlov equation and a tomographic problem with opaque parabolic objects

In contrast with 1+1 dimensional systems, integrable 2+1 systems are usually non-local, and integration based on the scattering transform corresponds to a special choice of integration constants. For the KP equation this study turned out to be rather non-trivial. We show that in case of the so-called Pavlov equation, with is a dispersionless 2+1 dimensional integrable model, the answer can be explained using some lemma from integral geometry.