Volume 15, Issue Supplement 1, August 2008, Pages 25 - 35
Complex Lie Symmetries for Variational Problems
Sajid Ali, Fazal M Mahomed, Asghar Qadir
Available Online 1 August 2008.
- https://doi.org/10.2991/jnmp.2008.15.s1.2How to use a DOI?
- 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.
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Cite this article
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 - https://doi.org/10.2991/jnmp.2008.15.s1.2 ID - Ali2008 ER -