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math.NA2024
Nonlinearity helps the convergence of the inverse Born series
Nicholas Defilippis, Shari Moskow, John C. Schotland
In previous work of the authors, we investigated the Born and inverse Born series for a scalar wave equation with linear and nonlinear terms, the nonlinearity being cubic of Kerr t…
math.NA2022
Born and inverse Born series for scattering problems with Kerr nonlinearities
Nicholas Defilippis, Shari Moskow, John C. Schotland
We consider the Born and inverse Born series for scalar waves with a cubic nonlinearity of Kerr type. We find a recursive formula for the operators in the Born series and prove the…