Malaysian Journal of Mathematical Sciences, May 2019, Vol. 13, No. 2
Symmetry Analysis, Nonlinearly Self-adjoint and Conservation Laws of a Generalized (2+1)-dimensional Klein-Gordon Equation
Magalakwe, G., Muatjetjeja, B., and Khalique, C. M.
Corresponding Email: Gabriel.Magalakwe@nwu.ac.za
Received date: 15 March 2018
Accepted date: 30 April 2019
Abstract:
We study a generalization of Klein-Gordon equation (gKGe) in (2+1) dimensions which has an arbitrary element. Lie group classification is
carried out on this equation. It is shown that gKGe admits a nine-dimensional Lie algebra of equivalence transformations and six-dimensional principal Lie algebra which has several possible extensions. The forms of the arbitrary element are linear, exponential, power-law nonlinearity and others. Closed-form solutions are obtained for some special cases of arbitrary element. Lastly, we derive conservation laws for the nonlinearly self-adjoint subclass of the gKGe.
Keywords: Lie group classification, Nonlinearly self-adjoint, generalized (2+1)-dimensional Klein-Gordon equation, Lie symmetry analysis, Exact solutions
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