An inverse problem for a nonlinear wave equation

The inverse problem of determining the coefficient under a nonlinear term of the equation, the main part of which is the wave operator, is considered. The properties of the solution of a direct problem are studied, in particular, the existence and uniqueness of a bounded solution in a neighborhood of a characteristic cone is established, and a structure of this solution is written out. The problem of finding an unknown coefficient is reduced to the problem of the integral geometry on a family of straight lines with a weight function that is invariant with respect to rotations around some fixed point. The uniqueness of the solution of the inverse problem is established and an algorithm of recovering the desired function is proposed.