New exact solutions and conservation laws of a class of Kuramoto Sivashinsky (KS) equations. Issue 1 (2nd January 2019)

• Record Type: Journal Article
• Authors: Govinder, K.S.; Narain, R.; Okeke, J.E.
• Is Part Of: Quaestiones mathematicae. Volume 42:Issue 1(2019)
• Page Start: 93
• Page End: 112
• Publication Date: 2019-01-02
• Subjects: 70G65 -- 76M60 -- 35B06 -- 70S10; Lie Symmetries -- extended-tanh method -- exact solutions -- conservation laws; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2018.1439542
• Languages: English
• ISSNs: 1607-3606

Abstract

Abstract: Lie symmetry method is used to perform detailed analysis on a class of KS equations. It is shown that the Lie algebra of the equation spanned by the vector fields of dilations in time and space are lost as a result of the linearity of the equation when n = 1. Symmetry reductions are carried out using each member of the optimal system. The reduced equations are further studied to obtain certain general solutions. Moreover, the conserved vectors are obtained through the application of Noether's theorem.