Nonlocal Symmetries and the Complete Symmetry Group of 1 + 1 Evolution Equations

DOI

10.2991/jnmp.2006.13.3.5How to use a DOI?

Abstract

The complete symmetry group of a 1 + 1 linear evolution equation has been demon- strated to be represented by the six-dimensional Lie algebra of point symmetries sl(2, R)?s W , where W is the three-dimensional Heisenberg-Weyl algebra. The infinite number of solution symmetries does not play a role in the complete specification of the equation. In the absence of a sufficient number of point symmetries which are not solution symmetries one must look to generalized or nonlocal symmetries to remove the deficit. This is true whether the evolution equation be linear or not. We report two Ansätze which provide a route to the determination of the required nonlocal symmetry necessary to supplement the point symmetries for the complete specification of two nonlinear 1 + 1 evolution equations which arise in the area of Financial Mathematics. The first of these, when reduced to its essential form, is the well-known Burgers’ equation.

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  - S.M. Myeni
AU  - P.G.L. Leach
PY  - 2006
DA  - 2006/08/01
TI  - Nonlocal Symmetries and the Complete Symmetry Group of 1 + 1 Evolution Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 377
EP  - 392
VL  - 13
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2006.13.3.5
DO  - 10.2991/jnmp.2006.13.3.5
ID  - Myeni2006
ER  -