Symmetry Reductions and Exact Solutions of a Variable Coefficient (2+1)-Zakharov-Kuznetsov Equation

Moleleki, L. D.; Johnpillai, A. G.; Khalique, C. M.

doi:10.3390/mca17020132

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Article

1 August 2012

8 Pages

Symmetry Reductions and Exact Solutions of a Variable Coefficient (2+1)-Zakharov-Kuznetsov Equation

and

International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, Republic of South Africa

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Math. Comput. Appl.2012, 17(2), 132-139;https://doi.org/10.3390/mca17020132

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Abstract

We study the generalized (2+1)-Zakharov-Kuznetsov (ZK) equation of time dependent variable coefficients from the Lie group-theoretic point of view. The Lie point symmetry generators of a special form of the class of equations are derived. We classify the Lie point symmetry generators to obtain the optimal system of onedimensional subalgebras of the Lie symmetry algebras. These subalgebras are then used to construct a number of symmetry reductions and exact group-invariant solutions to the underlying equation.

Keywords:

Generalized ZK equation; solitons; Lie symmetries; optimal system; symmetry reduction; group-invariant solutions

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