On the nonlocal Darboux transformation for the stationary axially symmetric Schr\"odinger and Helmholtz equations

The nonlocal Darboux transformation for the stationary axially symmetric Schr"odinger and Helmholtz equations is considered. Formulae for the nonlocal Darboux transformation are obtained and its relation to the generalized Moutard transformation is established. New examples of two - dimensional potencials and exact solutions for the stationary axially symmetric Schr"odinger and Helmholtz equations are obtained as an application of the nonlocal Darboux transformation.