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Some Reduction and Exact Solutions of a Higher‐Dimensional Equation

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  • Guangming Wang
  • Zhong Han

Abstract

The conservation laws of the (3 + 1)‐dimensional Zakharov‐Kuznetsov equation were obtained using Noether’s theorem after an interesting substitution u = vx to the equation. Then, with the aid of an obtained conservation law, the generalized double reduction theorem was applied to this equation. It can be verified that the reduced equation is a second order nonlinear ODE. Finally, some exact solutions of the Zakharov‐Kuznetsov equation were constructed after solving the reduced equation.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:597470
DOI: 10.1155/2014/597470
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