The nonlocal Darboux transformation of the 2D stationary Schrödinger equation and its relation to the Moutard transformation
arXiv:1303.5858
Abstract
The nonlocal Darboux transformation of the two - dimensional stationary Schrödinger equation is considered and its relation to the Moutard transformation is established. It is shown that a special case of the nonlocal Darboux transformation provides the Moutard transformation. New examples of solvable two - dimensional stationary Schrödinger operators with smooth potentials are obtained as an application of the nonlocal Darboux transformation.
15 pages; new references added in v2; corrected typos in v3
References in corpus (3)
- The exactly solvable two-dimensional stationary Schrödinger operators obtaining by the nonlocal Darboux transformation
- 2D Schrodinger Operator, (2+1) Systems and New Reductions. The 2D Burgers Hierarchy and Inverse Problem Data
- General Solution of the Two-Dimensional Intertwining Relations for Supercharges with Hyperbolic (Lorentz) Metrics