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In this work, we construct numerical solutions to an inverse problem of anonlinear Helmholtz equation defined in a spherical shell between twoconcentric spheres centered at the origin.Assuming that the values of theforward problem are known at sufficiently many points, we would like todetermine the form of the non-linear term on the right-hand side of theequation via its Chebyshev coefficients.

Numerical solutions to an inverse problem for a non-linear Helmholtz equation