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

Wang, Guangming; Han, Zhong

Abstr. Appl. Anal. 2014, Article ID 597470, 9 p. (2014).

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.

MSC:

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

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