On solvability by quadratures conditions for second order hyperbolic systems

Abstract

In the present work we consider boundary value problems for second order hyperbolic system with higher partial derivatives $u_{xy}$, $v_{xy}$ and $u_{xx}$, $v_{yy}$. The aim of the study is to find sufficient conditions for solvability of the considered problems by quadratures. We proposed a method for finding explicit solutions for the mentioned problems based on factorization of the equations in the original systems. As a result, in terms of the coefficients of these systems, we obtain 14 conditions for solvability by quadratures for each boundary value problem.