Geodesic
Asymptotic solutions of equations with complex characteristics
Sbornik. Mathematics, Tome 24 (1974) no. 2, pp. 159-207

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In this paper we give a method for constructing formal asymptotic solutions. This method uses in some sense “approximate solutions” of the equation of the characteristics and the transport equation. The construction of approximate solutions is brought abount by means of an analogue of the analytic Hamiltonian formalism in a complex phase space. Bibliography: 19 titles. 
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     title = {Asymptotic solutions of equations with complex characteristics},
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V. V. Kucherenko. Asymptotic solutions of equations with complex characteristics. Sbornik. Mathematics, Tome 24 (1974) no. 2, pp. 159-207. http://geodesic.mathdoc.fr/item/SM_1974_24_2_a0/