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The nonlinear Helmholtz equation (NLH) models the propagation of intense laser light in Kerr dielectrics such as water, silica or air.The key physical phenomenon of interest is self-focusing of the incoming beam which occurs because the index of refraction of the medium increases when the intensity of the field increases.Mathematical analysis of the NLH requires solution of a quasi-linear elliptic boundary value problem with nonhomogeneous and non-self-adjoint boundary conditions.This proves difficult for both theoretical study and numerical computation.