Abstract
We consider factorizations of the stationary and non-stationary Schrödinger equation in which are based on appropriate Dirac operators. These factorizations lead to a Miura transform which is an analogue of the classical one-dimensional Miura transform but also closely related to the Riccati equation. In fact, the Miura transform is a nonlinear Dirac equation. We give an iterative procedure which is based on fix-point principles to solve this nonlinear Dirac equation. The relationship to nonlinear Schrödinger equations like the Gross–Pitaevskii equation is highlighted.
§Dedicated to Richard Delanghe on the occasion of his 65th birthday.
Notes
§Dedicated to Richard Delanghe on the occasion of his 65th birthday.