Inverse problems for a quasilinear hyperbolic equation in the case of moving observation point

We consider two inverse coefficient problems for a quasilinear hyperbolic equation, where the additional information used for finding the coefficients is the values of the solution on some curve. (This corresponds to measurements performed at a moving observation point.) The unknown coefficient depends on the space variable in the first inverse problem and on the solution of the equation in the second inverse problem. We prove theorems of uniqueness of solution to the inverse problems.