On the nonlocal Darboux transformation for the stationary axially symmetric Schrödinger and Helmholtz equations

Abstract

The nonlocal Darboux transformation for the stationary axially symmetric Schrödinger 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 Schrödinger and Helmholtz equations are obtained as an application of the nonlocal Darboux transformation.

arXiv comment12 pages. arXiv admin note: text overlap with arXiv:1911.05023

References in corpus (4)

• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• Two-dimensional rational solitons and their blow-up via the Moutard transformation
• Generalization of SUSY Intertwining Relations: New Exact Solutions of Fokker-Planck Equation
• The exactly solvable two-dimensional stationary Schrödinger operators obtaining by the nonlocal Darboux transformation