Abstract
In this paper, the Lie group method is performed on a special dark fluid, the Chaplygin gas, which describes both dark matter and dark energy in the present universe. Based on an optimal system of one-dimensional subalgebras, similarity reductions and group invariant solutions are given. Finally, by means of Ibragimov’s method, conservation laws are obtained.
Highlights
Nonlinear partial differential equations (PDEs) play an indispensable role in the nature
Conservation laws can be obtained by variational principle or Hamilton’s principle [10, 11]
For the PDEs which do not have a Lagrangian, based on admitted symmetries [12], Ibragimov proposed the concept of the adjoint equation for the study of conservation laws by using conservation law theorem in [13]
Summary
Nonlinear partial differential equations (PDEs) play an indispensable role in the nature. A quite effective method among them, can get crucially explicit solutions of PDEs. On the other hand, an important issue regarding the PDEs is to obtain their conservation laws. We can apply conservation laws to obtain exact solutions of PDEs [14, 15]. The twocomponent Chaplygin gas equation can describe both dark matter and dark energy in the present universe [17, 18].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
