On the Origins of Symmetries of Partial Differential Equations: the Example of the Korteweg-de Vries Equation

DOI

10.2991/jnmp.2008.15.s1.5How to use a DOI?

Abstract

Type II hidden symmetries of partial differential equations () are extra symme- tries in addition to the inherited symmetries of the differential equations which arise when the number of independent and dependent variables is reduced by a Lie point symmetry. (Type I hidden symmetries arise in the increase of number of variables.) Unlike the case of ordinary differential equations, these symmetries do not arise from contact symmetries or nonlocal symmetries. In fact, we have previously shown that they are symmetries of other differential equations. However, in determining the origin of these symmetries we show that finding the origin of any symmetry of a pde is a non-trivial exercise. The example of the Korteweg–de Vries equation is used to illustrate this point.

Copyright

© 2008, 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  - Keshlan S. Govinder
AU  - Barbara Abraham-Shrauner
PY  - 2008
DA  - 2008/08/01
TI  - On the Origins of Symmetries of Partial Differential Equations: the Example of the Korteweg-de Vries Equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 60
EP  - 68
VL  - 15
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2008.15.s1.5
DO  - 10.2991/jnmp.2008.15.s1.5
ID  - Govinder2008
ER  -