Factorization of the nonlinear Schroedinger equation and applications
Complex Variables
2007-05-23 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.math/0509018,
title = {Factorization of the nonlinear Schroedinger equation and applications},
author = {Swanhild Bernstein},
journal= {arXiv preprint arXiv:math/0509018},
year = {2007}
}
Comments
22 pages