  In this paper we prove uniqueness for some parameter identification problems
for the JMGT equation, a third order in time quasilinear PDE in nonlinear
acoustics. The coefficients to be recovered are the space dependent
nonlinearity parameter, sound speed, and attenuation parameter, and the
observation available is a single time trace of the acoustic pressure on the
boundary. This is a setting relevant to several ultrasound based tomography
methods. Our approach relies on the Inverse Function Theorem, which requires to
prove that the forward operator is a differentiable isomorphism in
appropriately chosen topologies and with an appropriate choice of the
excitation.
