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Factorization of the nonlinear Schroedinger equation and applications

Swanhild Bernstein
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Abstract

We consider factorizations of the stationary and non-stationary Schroedinger equation in R^n 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 Schroedinger equations like the Gross-Pitaevskii equation are highlighted.

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Swanhild Bernstein. 2005-09-01. Factorization of the nonlinear Schroedinger equation and applications. https://arxiv.org/abs/math/0509018

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