A problem of recovering a special two dimension potential in a hyperbolic equation

We consider an inverse problem for partial differential equations of the second order related to recovering a coefficient (potential) in the lower term of this equations. It is supposed that the unknown potential is a trigonometric polynomial with respect to one of space variables with continuous coefficients of the other variable. The direct problem for the hyperbolic equation is the initial-boundary value problem for half-space $x > 0$ with zero initial Cauchy data and a special Neumann data at $x = 0$. We prove a local existence theorem for the inverse problem. The used method gives stability estimates for the solution to the direct and inverse problems and proposes a method of solving them.