Abstract
Conditional Lie symmetries of semi-linear 1D Schrödinger and diffusion equations are studied in case the mass (or the diffusion constant) is considered as an additional variable and/or where the couplings of the non-linear part have a non-vanishing scaling dimension. In this way, dynamical symmetries of semi-linear Schrödinger equations become related to certain subalgebras of a three-dimensional conformal Lie algebra (conf3)C. The representations of these subalgebras are classified and the complete list of conditionally invariant semi-linear Schrödinger equations is obtained. Applications to the phase-ordering kinetics of simple magnets and to simple particle-reaction models are briefly discussed.
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