Abstract
An inverse problem for a second-order hyperbolic equation containing two nonlinear termsis studied. The problem is to reconstruct the coefficients of the nonlinearities. The Cauchyproblem with a point source located at a point \(\mathbf {y}\) isconsidered. This point is a parameter of the problem and successively runs over a spherical surface \(S\) . It is assumed that the desired coefficients arenonzero only in a domain lying inside \(S\) . The trace of thesolution of the Cauchy problem on \(S\) is specified for allpossible values of \(\mathbf {y}\) and for times close to the arrival ofthe wave from the source to the points on the surface \(S\) ; this allows reducing the inverse problem underconsideration to two successively solved problems of integral geometry. Solution stability estimatesare found for these two problems.
