2019/01/08 by Tobias F. Illenseer, Illenseer, Tobias F.
Physics and Astronomy · #35K05 (Primary) #76M60 (Secondary) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1901.02231
openalex publication_date 2019/01/08 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28
A heat equation with non-constant diffusivity depending as a power law on the\nspatial variable is analysed using Lie's method to identify classical point\nsymmetries. It is shown that the group invariant solutions of a\nfour-dimensional symmetry subgroup can be decomposed into three different\nclasses. These admit explicit solutions which can either be expressed in terms\nof Bessel functions, confluent hypergeometric functions or Coulomb wave\nfunctions.\n