Gruppo di Fisica Statistica

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.