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Generalized solitary and periodic wave solutions to a \((2+1)\)-dimensional Zakharov-Kuznetsov equation. (English) Zbl 1203.35205

Summary: The Exp-function method is employed to the Zakharov-Kuznetsov equation as a \((2+1)\)-dimensional model for nonlinear Rossby waves. The observation of solitary wave solutions and periodic wave solutions constructed from the exponential function solutions reveal that our approach is very effective and convenient. The obtained results may be useful for better understanding the properties of two-dimensional coherent structures such as atmospheric blocking events.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
35C08 Soliton solutions
35A24 Methods of ordinary differential equations applied to PDEs
35B10 Periodic solutions to PDEs
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