Construction of invisible defects in acoustic waveguides

In this talk, we consider a time harmonic acoustic problem in a locally perturbed waveguide. We are interested in a situation where an observer generates incident propagative waves from $-\infty$ and measures the resulting scattered field at $-\infty$ and/or $+\infty$. We explain how to construct perturbations of the waveguide such that the scattered field is exponentially decaying at $-\infty$ and/or at $+\infty$, so that in practice, these defects are invisible to the observer.