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Dynamical symmetries of semi-linear Schrödinger and diffusion equations

Stoimen Stoimenov·Malte Henkel
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Abstract

Conditional and 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. 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 conf_3 are classified and the complete list of conditionally invariant semi-linear Schrödinger equations is obtained. Possible applications to the dynamical scaling behaviour of phase-ordering kinetics are discussed.

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BibTeXRIS

Stoimen Stoimenov, Malte Henkel. 2005-05-17. Dynamical symmetries of semi-linear Schrödinger and diffusion equations. https://doi.org/10.1016/j.nuclphysb.2005.06.017

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