Some reduction and exact solutions of a higher-dimensional equation. (English) Zbl 1474.35574

Summary: The conservation laws of the \((3 + 1)\)-dimensional Zakharov-Kuznetsov equation were obtained using Noether’s theorem after an interesting substitution \(u = v_x\) 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.


35Q53 KdV equations (Korteweg-de Vries equations)
35A30 Geometric theory, characteristics, transformations in context of PDEs
Full Text: DOI


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