Application of the homotopy perturbation method to Zakharov-Kuznetsov equations. (English) Zbl 1189.65244

Summary: The aim of this paper is to apply the homotopy perturbation method (HPM) to solve the Zakharov-Kuznetsov \(ZK(m,n,k)\) equations. The two special cases, \(ZK(2, 2, 2)\) and \(ZK(3, 3, 3)\), are chosen to show the ability of the method. General formulas for the solutions of \(ZK(m,n,k)\) are established. The results reveal that the method is very effective and simple.


65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
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