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Lie symmetries of semi-linear Schrödinger equations and applications

Stoimen Stoimenov·Malte Henkel
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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.

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Stoimen Stoimenov, Malte Henkel. 2005-12-08. Lie symmetries of semi-linear Schrödinger equations and applications. https://doi.org/10.1088/1742-6596%2F40%2F1%2F018

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