THE SOLUTION OF CAUCHY PROBLEM FOR THE HYPERBOLIC DIFFERENTIAL EQUATIONS OF THE FOURTH ORDER BY THE RIMAN METHOD

Abstract

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.