Equivalence and symmetries for variable coefficient linear heat type equations. I


Gungor F.

JOURNAL OF MATHEMATICAL PHYSICS, cilt.59, 2018 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 59 Konu: 5
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1063/1.5000589
  • Dergi Adı: JOURNAL OF MATHEMATICAL PHYSICS

Özet

A systematic and unified approach to transformations and symmetries of a class of variable coefficient heat type linear partial differential equations (PDEs) is presented. The complete symmetry group classification is re-performed in the current context. A useful criterion which is necessary and sufficient for being reducible to the standard heat equation by point transformations is established. A similar criterion is also valid for the equations to have a four- or six-dimensional symmetry group (nontrivial symmetry groups). In this situation, the basis elements are listed in terms of coefficients. A number of illustrative examples are given. In particular, some applications from the recent literature are re-examined in our new approach. Multidimensional parabolic PDEs of heat and Schrodinger type are also considered. Published by AIP Publishing.