| Abstract: |
| In this talk, we will discuss inverse boundary problems for semilinear Schrodinger equations on smooth compact Riemannian manifolds of dimension two and higher with smooth boundary, at a large fixed frequency. We will demonstrate that certain classes of cubic nonlinearities are uniquely determined from the knowledge of the nonlinear Dirichlet-to-Neumann map at a large fixed frequency on quite general Riemannian manifolds. In particular, in contrast to the previous results available, here the manifolds need not satisfy any product structure, may have trapped geodesics, and the geodesic ray transform need not be injective. Only a mild assumption about the geometry of intersecting geodesics is required. This is joint work with Shiqi Ma, Suman Kumar Sahoo, Mikko Salo, and Simon St-Amant. |
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