The new Lie point reductions and similarity solutions for the Gordon-type equation of the Milne metric

被引：0
|
作者：
Nadjafikhah, Mehdi [1 ]
Mobarra, Leila Hamedi [2 ]
机构：
[1] Iran Univ Sci & Technol, Sch Math, Tehran, Iran
[2] Payamnoor Univ, Dept Sci, Tehran 193954697, Iran
来源：
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS | 2015年 / 12卷 / 05期
关键词：
Milne metric; Gordon-type equation; Lie point reduction; similarity solutions; optimal system of subalgebras;
D O I：
10.1142/S021988781550053X
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
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.
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页数：11
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