GEOMETRIC OPTICS FOR 3D-HARTREE-TYPE EQUATION WITH COULOMB POTENTIAL

This article considers a family of 3D-Hartree-type equation with Coulomb potential ∣x∣−1, whose initial data oscillates so that a caustic appears. In the linear geometric optics case, by using the Lagrangian integrals, a uniform description of the solution outside the caustic, and near the caustic are obtained.