Scattering transform for multidimensional dispersionless systems. Exact results for the Pavlov equation.

Multidimensional integrable systems are usually non-local, therefore the solutions of the Cauchy problem depend on a proper choice of intergration constants. The inverse scattering transform usually prescribe a special choice of these constants. We calculate this choice for the model example of the Pavlov equation. The final answer can be explained using a lemma form integral geometry.