ABSTRACT
In the following, we are only interested in asymptotic solutions and do not study whether the asymptotic solutions constructed here are close to exact solutions.
Construction o f the asymptotic solution. We seek the solution of problem (5.1) with the help of the canonical operator. We use the construction of the canonical operator given in Chapter 3. First, note that the initial data in (5.1 ) is
is the initial Lagrangian manifold in the phase space Щ*р-The measure άμo in (5.5) is given by
Indeed, Ло is projected diffeomorphically on the ρ-plane and is covered by a single nonsingular chart with canonical coordinates {q^pj) = q, (I = 0). Hence the canonical operator with measure dpo on A0 has the form (5.5).
