Vestnik of Samara University. Natural Science SeriesVestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University765310.18287/2541-7525-2019-25-3-33-38UnknownTHE SOLUTION OF CAUCHY PROBLEM FOR THE HYPERBOLIC DIFFERENTIAL EQUATIONS OF THE FOURTH ORDER BY THE RIMAN METHODYakovlevaJu. O.<p>Candidate of Physical and Mathematical Sciences, associate professor,associate professor of the Department of Higher Mathematics</p>morenov@ssau.ruhttps://orcid.org/0000-0002-9839-3740TarasenkoA. V.<p>Candidate of Physical and Mathematical Sciences, associate professor of the Department of Higher Mathematics</p>morenov@ssau.ruhttps://orcid.org/0000-0002-0487-8262Samara State Technical University16092019253333817022020Copyright © 2019, Yakovleva J.O., Tarasenko A.V.2019<p>In the article the Cauchy problem for the one system of the differential equations of the fourth order is received in the plane of two independent variables. This system of the hyperbolic differential equations of the fourth order does not contain derivatives less than the fourth order. The regular solution of the Cauchy problem for the system of the hyperbolic differential equations of the fourth order is explicitly built. The solution of the Cauchy problem for the system of the hyperbolic differential equations of the fourth order is found by the Riman method. In the paper the matrix of Riman for the system of the hyperbolic differential equations of the fourth order is constructed also. The matrix of Riman is expressed through hypergeometrical functions of matrix argument.</p>система дифференциальных уравнений гиперболического типа четвертого порядка, гиперболическое уравнение, регулярное решение, метод Римана, задача Коши, функция Римана, матрица Римана, гипергеометрические функции матричного аргумента.system of hyperbolic differential equations of the fourth order, hyperbolic equation, regular solution, method of Riman, Cauchy problem, function of Riman, matrix of Riman, hypergeometrical functions of matrix argument.[1] Trusdell K. Pervonachal’nyi kurs ratsional’noi mekhaniki sploshnykh sred [Initial course of rational mechanics of solid media]. Moscow: Mir, 1975, 592 p. Available at: <a href='https://www.studmed.ru/trusdell-k-pervonachalnyy-kurs-racionalnoy-mehaniki-sploshnyh-sred_f4d30841e26.html'>https://www.studmed.ru/trusdell-k-pervonachalnyy-kurs-racionalnoy-mehaniki-sploshnyh-sred_f4d30841e26.html</a> [in Russian].][[2] Oskolkov A.P. 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