Articles in peer-reviewed journals
|Dynamical symmetries of semi-linear Schroedinger and diffusion equations|
|Stoimenov S., Henkel M.|
|Nuclear Physics B 723 (2005) 205|
|DOI : 10.1016/j.nuclphysb.2005.06.017|
|ArXiv : math-ph/0504028 [PDF]|
Conditional and Lie symmetries of semi-linear 1D Schroedinger 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 Schroedinger equations become related to the parabolic and almost-parabolic subalgebras of a three-dimensional conformal Lie algebra (conf3)â"`. 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 (conf3) â"` are classified and the complete list of conditionally invariant semi-linear Schroedinger equations is obtained. Possible applications to the dynamical scaling behaviour of phase-ordering kinetics are discussed.