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Application of the homotopy analysis method to solving nonlinear evolution equations. (Chinese. English summary) Zbl 1202.65130
Summary: We obtain a class of approximate periodic solutions for the \((2+1)\)-dimensional modified Zakharov-Kuznetsov equation by using the homotopy analysis method (HAM). The solutions we obtained agree with the exact solutions. The results indicate that the HAM is still valid for solving a class of higher dimensional evolution equations. We also made some efforts to extend the HAM to find the analytic solutions for more nonlinear evolution equations in an easier way.

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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