Research articles
ScienceAsia 40 (2014): 451455 doi:
10.2306/scienceasia15131874.2014.40.451
On the solutions and conservation laws for the SharmaTassoOlver equation
Andrew Gratien Johnpillai^{a}, Chaudry Masood Khalique^{b,*}
ABSTRACT: We study the SharmaTassoOlver equation from the Lie symmetry point of view. We derive the Lie point symmetry generators of the equation and classify them to obtain the optimal system of onedimensional subalgebras of the Lie symmetry algebra of the equation. These subalgebras are then used to construct symmetry reductions for the equation. We obtain the general solution of the nonlinear secondorder ordinary differential equation which results from the symmetry reduction for the travelling wave groupinvariant solutions of the equation by transforming it into a linear thirdorder ordinary differential equation through a Riccati transformation. Then we show that one can easily obtain the travelling wave exact groupinvariant solutions for the underlying equation by using the general solution of the linearized thirdorder ordinary differential equation and the Riccati transformation. We also construct conservation laws for the underlying equation by making use of the multiplier method.
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^{a} 
Department of Mathematics, Eastern University, 30350, Sri Lanka 
^{b} 
International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, NorthWest University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa 
* Corresponding author, Email: Masood.Khalique@nwu.ac.za
Received 3 Apr 2014, Accepted 29 Sep 2014
