Dynamical symmetries of semi-linear Schrödinger and diffusion equations

  • Stoimenov S
  • Henkel M
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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 (conf3)ℂ. 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 (conf3)ℂare 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. © 2005 Elsevier B.V. All rights reserved.

Author-supplied keywords

  • Conditional symmetry
  • Conformal group
  • Non-linear Schrödinger equation
  • Non-linear diffusion equation
  • Phase-ordering kinetics
  • Schrödinger group

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Authors

  • Stoimen Stoimenov

  • Malte Henkel

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