Complex Lie Symmetries for Variational Problems

DOI

10.2991/jnmp.2008.15.s1.2How to use a DOI?

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

© 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  - Sajid Ali
AU  - Fazal M Mahomed
AU  - Asghar Qadir
PY  - 2008
DA  - 2008/08/01
TI  - Complex Lie Symmetries for Variational Problems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 25
EP  - 35
VL  - 15
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2008.15.s1.2
DO  - 10.2991/jnmp.2008.15.s1.2
ID  - Ali2008
ER  -