Open AccessOn the Asymptotics of Solutions of the Klein - Gordon - Fock Equation with Meromorphic Coefficients in the Neighborhood of Infinity
Author(s) -
М. В. Коровина,
Hovik A. Matevossian,
Ilya Smirnov,
В.И. Смирнов
Publication year - 2021
Publication title -
journal of physics: conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
ISSN - 1742-6588
DOI - 10.1088/1742-6596/1990/1/012017
Subject(s) - meromorphic function , holomorphic function , mathematics , mathematical analysis , infinity , order (exchange) , pure mathematics , finance , economics
In this paper we investigate the construction of uniform asymptotics of solutions for the Klein-Gordon-Fock boundary value problem with meromorphic coefficients as t → ∞. The difficulty in solving these problems is due to the fact that infinity, as known, is an irregular singular point of such equations. In the case of holomorphic coefficients, the order of degeneracy will be at most two, and in the case of meromorphic coefficients it can be arbitrary, and it will depend on the order of the poles of the meromorphic coefficients. The main method for constructing asymptotics in the neighbourhood of an irregular singular point is the method of resurgent analysis, which is based on the Laplace-Borel integral transform. Using this method, in this paper, a uniform asymptotics of the problem under consideration is constructed in a neighborhood of infinity for arbitrary meromorphic (or holomorphic) coefficients.