Article

New exact solutions and conservation laws of a class of Kuramoto Sivashinsky (KS) equations

Published in: Quaestiones Mathematicae
Volume 42 , issue 1 , 2019 , pages: 93–112

DOI: 10.2989/16073606.2018.1439542

Author(s): K.S. Govinder Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, South Africa , R. Narain Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, South Africa , J.E. Okeke Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, South Africa

Keywords: 70G65 , 76M60 , 35B06 , 70S10 , 70G65 , 76M60 , 35B06 , 70S10

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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.

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