 |
Bulgarian Journal of Physics
Print: 1310-0157 Online: 1314-2666
|
RECOGNIZED BY THE EUROPEAN PHYSICAL SOCIETY 
Bulg. J. Phys. vol.33 no.s2 (2006), pp. 223-226
Lie Symmetries of Semi-Linear Schrödinger and Diffusion
S. Stoimenov1, M. Henkel2
1Laboratoire de Physique des Matériaux (CNRS UMR 7556), Université Henri Poincaré Nancy I, B.P.239, F-54506 Vanduvre lès Nancy Cede
2Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences,1784 Sofia, Bulgaria
go back1Laboratoire de Physique des Matériaux (CNRS UMR 7556), Université Henri Poincaré Nancy I, B.P.239, F-54506 Vanduvre lès Nancy Cede
2Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences,1784 Sofia, Bulgaria
Abstract. Conditional Lie symmetries of semi-linear 1D Schrödinger 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 Schrödinger equations become related to the parabolic and almost-parabolic subalgebras of a three-dimensional conformal Lie algebra (conf3)C. The corresponding representations of the parabolic and almost-parabolic subalgebras of (conf3)C are classified and the complete list of conditionally invariant semi-linear Schrödinger equations is obtained.