On structural properties of solutions of hyperbolic systems of partial differential equations of the first order

The formula is found for integral representation of solutions of the system \[ \begin{aligned} \frac{\partial u}{\partial x}+\frac{\partial u^*}{\partial t}&=au+a^*u^*+f,
\frac{\partial u}{\partial t}+\frac{\partial u^*}{\partial x}&=bu+b^*u^*+f^*. \end{aligned} \tag{1} \] This integral representation permits to establish structural properties of the solutions of the system (1).