Conditional and Lie symmetries of semi-linear 1D Schr\"odinger and diffusion
equations are studied if the mass (or the diffusion constant) is considered as
an additional variable. In this way, dynamical symmetries of semi-linear
Schr\"odinger equations become related to the parabolic and almost-parabolic
subalgebras of a three-dimensional conformal Lie algebra conf_3. We consider
non-hermitian representations and also include a dimensionful coupling constant
of the non-linearity. The corresponding representations of the parabolic and
almost-parabolic subalgebras of conf_3 are classified and the complete list of
conditionally invariant semi-linear Schr\"odinger equations is obtained.
Possible applications to the dynamical scaling behaviour of phase-ordering
kinetics are discussed.
Publié le : 2005-04-08
Classification:
Mathematical Physics,
Condensed Matter - Statistical Mechanics,
High Energy Physics - Theory,
Nonlinear Sciences - Exactly Solvable and Integrable Systems
@article{0504028,
author = {Stoimenov, Stoimen and Henkel, Malte},
title = {Dynamical symmetries of semi-linear Schr\"odinger and diffusion
equations},
journal = {arXiv},
volume = {2005},
number = {0},
year = {2005},
language = {en},
url = {http://dml.mathdoc.fr/item/0504028}
}
Stoimenov, Stoimen; Henkel, Malte. Dynamical symmetries of semi-linear Schr\"odinger and diffusion
equations. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0504028/