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New exact traveling wave solutions of the (\(2+1\))-dimensional Zakharov-Kuznetsov (ZK) equation. (English) Zbl 1199.34005

Summary: The homogeneous balance method is used to construct new exact traveling wave solutions for the \((2+1)\) dimensional Zakharov-Kuznetsov (ZK) equation. Many new exact traveling wave solutions are successfully obtained. This method is straightforward and concise, and it can also be applied to other nonlinear evolution equations.

MSC:

34A05 Explicit solutions, first integrals of ordinary differential equations
34B40 Boundary value problems on infinite intervals for ordinary differential equations
35Q51 Soliton equations
35C07 Traveling wave solutions
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