A particular solution of a problem for a system of equations from mechanics with nonsmooth Cauchy condition

In this article, we study a mixed problem in quarter-plane for system of differential equations, which describes vibrations string from viscoelastic material, corresponds to Maxwell material. At the bottom boundary, Cauchy conditions are specified, and one them has discontinuity first kind at point. A smooth boundary condition is set side boundary. The Klein – Gordon Fock equation derived system’s functions. We find particular solution two ways. method builds it an explicit analytical form (with continuation function), second constructs as integral using characteristics (without function). Conditions established under sufficient smoothness.