Geodesic
On~normal forms of nonsmoothness of solutions of hyperbolic equations
Izvestiya. Mathematics , Tome 30 (1988) no. 3, pp. 615-628

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Special functions are indicated that describe the smoothness asymptotics of the fundamental solution of a strictly hyperbolic equation in a neighborhood of the wave front set (assuming finite multiplicity of the critical points of the generating function). The special functions are given in the form of integrals of closed differential forms over (generally speaking, relative) homology classes of a complex manifold that depends on a point outside the wave front set. Bibliography: 24 titles. 
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     author = {A. N. Varchenko},
     title = {On~normal forms of nonsmoothness of solutions of hyperbolic equations},
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A. N. Varchenko. On~normal forms of nonsmoothness of solutions of hyperbolic equations. Izvestiya. Mathematics , Tome 30 (1988) no. 3, pp. 615-628. http://geodesic.mathdoc.fr/item/IM2_1988_30_3_a8/