Asymptotic solution of the Cauchy problem for equations with complex characteristics

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Abstract

Differential equations with a small parameter in the derivative are considered. A method is developed for constructing formal asymptotic solutions for the case of complex characteristics. For this a new class of manifolds is introduced which is a natural generalization of real Lagrangian manifolds to the complex case. The theory of the canonical Maslov operator is constructed in this class of manifolds. Asymptotic solutions are expressed in terms of the canonical Maslov operator.

Original languageEnglish
Pages (from-to)24-81
Number of pages58
JournalJournal of Soviet Mathematics
Volume13
Issue number1
DOIs
StatePublished - Jan 1980

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