Volume 13, Issue 3, August 2006, Pages 377 - 392
Nonlocal Symmetries and the Complete Symmetry Group of 1 + 1 Evolution Equations
S.M. MYENI 0, P.G.L. LEACH 1
0School of Mathematical Sciences, Howard College
1School of Mathematical Sciences, Howard College
Received 29 August 2005, Accepted 12 January 2006, Available Online 1 August 2006.
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- 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.
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Cite this article
TY - JOUR AU - S.M. MYENI AU - P.G.L. LEACH PY - 2006 DA - 2006/08 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 - https://doi.org/10.2991/jnmp.2006.13.3.5 ID - MYENI2006 ER -