Dynamical symmetries of semi-linear Schrödinger and diffusion equations

Details Dynamical symmetries of semi-linear Schrödinger and diffusion equations Dynamical symmetries of semi-linear Schrödinger and diffusion equations

2005-04-08

arxiv.org/abs/math-ph/0504028v2

Nucl. Phys. B723, 205-233 (2005)

Physics

Mathematical Physics

Latex2e, 27 pages, 1 figure

Scientific paper

10.1016/j.nuclphysb.2005.06.017

Conditional and 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. 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 Schr\"odinger equations is obtained. Possible applications to the dynamical scaling behaviour of phase-ordering kinetics are discussed.

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