Affiliation:
1. School of Mathematics, Iran University of Science and Technology, Narmak-16, Tehran, I. R., Iran
2. Science Department, Payamnoor University, 19395-4697 Tehran, I. R., Iran
Abstract
In this paper, three similarity solutions of a mathematical model for the gravitational waves of the Milne expanding empty spacetime, namely, the Gordon-type equation of the Milne metric will be determined. This equation is a linear second-order partial differential equation, dependent on a functional parameter. Formerly, some Lie reductions of the equation have been found, only for the special cases of its parameter. In this work, by applying a symmetry method for the Gordon-type equation, its new Lie reductions will be found, in the general form of the parameter. Then, its three similarity solutions will be presented.
Publisher
World Scientific Pub Co Pte Lt
Subject
Physics and Astronomy (miscellaneous)