Lagrangian manifolds and complex vector bundles, corresponding to semi-classical solutions for equations with delta-type singularities

Semi-classical asymptotics of solutions for a wide class of evolution equations with smooth coefficients are connected with geometric objects — Lagrangian surfaces or complex vector bundles over isotropic manifolds. If the coefficients of the equations contain singularities (or depend singularly on a small parameter of the problem), geometric objects are rebuilt on the sets corresponding to the supports of these singularities. The talk discusses the form of asymptotic solutions and rearrangements of geometric objects for certain examples of evolutionary problems with singularities.