# Lie symmetries of semi-linear Schr\\"odinger equations and applications

Source: [Lie symmetries of semi-linear Schr\\"odinger equations and applications](<https://www.sota2.com/research/paper/68fa20577a2b558e29330587>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-23T21:37:04.100Z

Authors: Stoimen Stoimenov, Malte Henkel

Published: 2005-12-08T14:48:36.000Z

## Abstract

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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/math-ph/0512025>)

[PDF](<https://arxiv.org/pdf/math-ph/0512025.pdf>)