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title:
 
Complex Lie Symmetries for Variational Problems
publication:
 
JNMP
volume-issue:   15 - Supplement 1
pages:   25 - 35
ISSN:
  1402-9251
DOI:
  doi:10.2991/jnmp.2008.15.s1.2 (how to use a DOI)
author(s):
 
Sajid Ali, Fazal M Mahomed, Asghar Qadir
publication date:
 
August 2008
abstract:
 
We present the use of complex Lie symmetries in variational problems by defining a complex Lagrangian and considering its Euler-Lagrange ordinary differential equation. This Lagrangian results in two real “Lagrangians” for the corresponding system of partial differential equations, which satisfy Euler-Lagrange like equations. Those complex Lie symmetries that are also Noether symmetries (i.e. symmetries of the complex Lagrangian) result in two real Noether symmetries of the real “Lagrangians”. Also, a complex Noether symmetry of a second order complex ordinary differential equation results in a double reduction of the complex ordinary differential equation. This implies a double reduction in the corresponding system of partial differential equations.
copyright:
 
© The authors.
This article is distributed under the terms of the Creative Commons Attribution License 4.0, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited. See for details: https://creativecommons.org/licenses/by-nc/4.0/
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