International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2578

Full Length Research Paper

Symmetry reductions and exact solutions of a variable coefficient (2+1)-Zakharov-Kuznetsov equation

L. D. Moleleki, A. G. Johnpillai and C. M. Khalique*
Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, Republic of South Africa.
Email: [email protected]

  •  Accepted: 16 November 2011
  •  Published: 23 December 2011

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 one-dimensional 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.

 

Key words: Generalized ZK equation, solitons, Lie symmetries, optimal system, symmetry reduction, group-invariant solutions.

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