首页|Increasing stability in the linearized inverse Schrodinger potential problem with power type nonlinearities*
Increasing stability in the linearized inverse Schrodinger potential problem with power type nonlinearities*
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NSTL
We consider increasing stability in the inverse Schrodinger potential problem with power type nonlinearities at a large wavenumber. Two linearization approaches, with respect to small boundary data and small potential function, are proposed and their performance on the inverse Schrodinger potential problem is investigated. It can be observed that higher order linearization for small boundary data can provide an increasing stability for an arbitrary power type nonlinearity term if the wavenumber is chosen large. Meanwhile, linearization with respect to the potential function leads to increasing stability for a quadratic nonlinearity term, which highlights the advantage of nonlinearity in solving the inverse Schrodinger potential problem. Noticing that both linearization approaches can be numerically approximated, we provide several reconstruction algorithms for the quadratic and general power type nonlinearity terms, where one of these algorithms is designed based on boundary measurements of multiple wavenumbers. Several numerical examples shed light on the efficiency of our proposed algorithms.
increasing stabilityinverse Schrodinger potential problempower type nonlinearitiesreconstruction algorithmsHELMHOLTZ-EQUATIONATTENUATIONSCATTERING
NSTL
