  We study an inverse problem for a coupled system of semilinear Helmholtz
equations where we are interested in reconstructing multiple coefficients in
the system from internal data measured in applications such as thermoacoustic
imaging. We derive results on the uniqueness and stability of the inverse
problem in the case of small boundary data based on the technique of first- and
higher-order linearization. Numerical simulations are provided to illustrate
the quality of reconstructions that can be expected from noisy data.
