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

Recovering coefficients in a system of semilinear Helmholtz equations from internal data