Lie Symmetries, Painlev\’{e} analysis and global
dynamics for the temporal equation of radiating stars
Abstract
We study the temporal equation of radiating stars by using three
powerful methods for the analysis of nonlinear differential equations.
Specifically, we investigate the global dynamics for the given master
ordinary differential equation to understand the evolution of solutions
for various initial conditions as also to investigate the existence of
asymptotic solutions. Moreover, with the application of Lie’s theory, we
can reduce the order of the master differential equation, while an exact
similarity solution is determined. Finally, the master equation
possesses the Painlev\’{e} property, which means that
the analytic solution can be expressed in terms of a Laurent expansion.