Lie symmetries of semi-linear Schrödinger equations and applications

Details Lie symmetries of semi-linear Schrödinger equations and applications Lie symmetries of semi-linear Schrödinger equations and applications

2005-12-08

arxiv.org/abs/math-ph/0512025v1

J.Phys.Conf.Ser. 40 (2006) 144-149

Physics

Mathematical Physics

Latex 2e, 6 pages, 1 figure, IOP macros, presented the the summer school `Ageing and the glass transition' Luxemburg 18-24 sep

Scientific paper

10.1088/1742-6596/40/1/018

Conditional Lie symmetries of semi-linear 1D Schr\"odinger 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 Schr\"odinger 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 Schr\"odinger 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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