Lie symmetries of semi-linear Schr\"odinger equations and applications
Stoimenov, Stoimen ; Henkel, Malte
arXiv, 0512025 / Harvested from arXiv
Text on arXiv
Conditional 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. 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. Applications to the phase-ordering kinetics of simple magnets and to simple particle-reaction models are briefly discussed.
Publié le : 2005-12-08
Classification:  Mathematical Physics,  Condensed Matter - Statistical Mechanics,  High Energy Physics - Theory,  Nonlinear Sciences - Exactly Solvable and Integrable Systems 
@article{0512025,
     author = {Stoimenov, Stoimen and Henkel, Malte},
     title = {Lie symmetries of semi-linear Schr\"odinger equations and applications},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0512025}
}

Stoimenov, Stoimen; Henkel, Malte. Lie symmetries of semi-linear Schr\"odinger equations and applications. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0512025/