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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.

35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations
35C08Soliton solutions of PDE
35A24Methods of ordinary differential equations for PDE
35B10Periodic solutions of PDE
Full Text: DOI
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