Factorization of the nonlinear Schroedinger equation and applications
Bernstein, Swanhild
arXiv, 0509018 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-09-01
Classification:  Mathematics - Complex Variables,  Mathematical Physics,  30G35,  35J10,  35F30,  35Q55 
@article{0509018,
     author = {Bernstein, Swanhild},
     title = {Factorization of the nonlinear Schroedinger equation and applications},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0509018}
}

Bernstein, Swanhild. Factorization of the nonlinear Schroedinger equation and applications. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0509018/