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Abstract We consider an inverse boundary value problem for a semilinear wave equation on a time-dependent Lorentzian manifold with time-like boundary. The time-dependent coefficients of the nonlinear terms can be recovered in the interior from the knowledge of the Neumann-to-Dirichlet map. Either distorted plane waves or Gaussian beams can be used to derive uniqueness.
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We characterize the kernel of the mixed ray transform on simple 2-dimensional Riemannian manifolds, that is, on simple surfaces for tensors of any order.
