Multiscale scattering in nonlinear Kerr-type media

We propose a multiscale approach for nonlinear Helmholtz problem with possible oscillations in the Kerr coefficient, refractive index, and diffusion coefficient. The method does not rely on structural assumptions coefficients combines technique known as Localized Orthogonal Decomposition an adaptive iterative approximation of nonlinearity. rigorously analyze terms well-posedness convergence properties based suitable initial data discretization parameters. Numerical examples illustrate theoretical error estimates underline practicability approach.