Lie symmetries of semi-linear Schrödinger equations and applications
arXiv:math-ph/0512025 · doi:10.1088/1742-6596/40/1/018
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 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 Schrödinger equations is obtained. Applications to the phase-ordering kinetics of simple magnets and to simple particle-reaction models are briefly discussed.
arXiv commentLatex 2e, 6 pages, 1 figure, IOP macros, presented the the summer school `Ageing and the glass transition' Luxemburg 18-24 sept 2005
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