Geodesic
The solution of Cauchy problem for the hyperbolic differential equations of the fourth order by the Riman method
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 25 (2019) no. 3, pp. 33-38

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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.
Keywords: system of hyperbolic differential equations of the fourth order, hyperbolic equation, regular solution, method of Riman, Cauchy problem, function of Riman, hypergeometrical functions of matrix argument.
Mots-clés : matrix of Riman 
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     author = {J. O. Yakovleva and A. V. Tarasenko},
     title = {The solution of {Cauchy} problem for the hyperbolic differential equations of the fourth order by the {Riman} method},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {33--38},
     publisher = {mathdoc},
     volume = {25},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2019_25_3_a3/}
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J. O. Yakovleva; A. V. Tarasenko. The solution of Cauchy problem for the hyperbolic differential equations of the fourth order by the Riman method. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 25 (2019) no. 3, pp. 33-38. http://geodesic.mathdoc.fr/item/VSGU_2019_25_3_a3/