A Symmetry Connection Between Hyperbolic and Parabolic Equations

DOI

10.2991/jnmp.1996.3.3-4.8How to use a DOI?

Abstract

We give ansatzes obtained from Lie symmetries of some hyperbolic equations which reduce these equations to the heat or Schrödinger equations. This enables us to construct new solutions of the hyperbolic equations using the Lie and conditional symmetries of the parabolic equations. Moreover, we note that any equation related to such a hyperbolic equation (for example the Dirac equation) also has solutions constructed from the heat and Schrödinger equations.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Peter Basarab-Horwath
PY  - 1996
DA  - 1996/09/02
TI  - A Symmetry Connection Between Hyperbolic and Parabolic Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 311
EP  - 318
VL  - 3
IS  - 3-4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1996.3.3-4.8
DO  - 10.2991/jnmp.1996.3.3-4.8
ID  - Basarab-Horwath1996
ER  -