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    Symmetry reductions, exact solutions and conservation laws of a variable coefficient (2+1)-dimensional zakharov-kuznetsov equation

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    Date
    2011
    Author
    Moleleki, Letlhogonolo Daddy
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    Abstract
    This research studies two nonlinear problems arising in mathematical physics. Firstly the Korteweg-de Vrics-Burgers equation is considered. Lie symmetry method is used to obtain t he exact solutions of Korteweg-de Vries-Burgers equation. Also conservation laws are obtained for this equation using the new conservation theorem. Secondly, we consider the generalized (2+ 1)-dimensional Zakharov-Kuznctsov (ZK) equation of time dependent variable coefficients from the Lie group-theoretic point of view. We classify the Lie point symmetry generators to obtain the optimal system of one-dimensional subalgebras of t he Lie symmetry algebras. These subalgebras arc then used to construct a number of symmetry reductions and exact group-invariant solutions of the ZK equation. We utilize the new conservation theorem to construct the conservation laws of t he ZK equation.
    URI
    http://hdl.handle.net/10394/14404
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    • Natural and Agricultural Sciences [2757]

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