An integrable time-dependent non-linear Schr\"odinger equation
Horváthy, P. A. ; Yéra, J. -C.
arXiv, 9806017 / Harvested from arXiv
Text on arXiv
The cubic non-linear Schr\"odinger equation (NLS), where the coefficient of the non-linear term can be a function $F(t,x)$, is shown to pass the Painlev\'e test of Weiss, Tabor, and Carnevale only for $F=(a+bt)^{-1}$, where $a$ and $b$ constants. This is explained by transforming the time-dependent system into the ordinary NLS (with $F=\const$.) by means of a time-dependent on-linear transformation, related to the conformal properties of non-relativistic space-time.
Publié le : 1998-06-30
Classification:  Mathematical Physics,  High Energy Physics - Theory 
@article{9806017,
     author = {Horv\'athy, P. A. and Y\'era, J. -C.},
     title = {An integrable time-dependent non-linear Schr\"odinger equation},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9806017}
}

Horváthy, P. A.; Yéra, J. -C. An integrable time-dependent non-linear Schr\"odinger equation. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9806017/