中文摘要：

利用同伦分析法求解了（2＋1）维改进的Zakharov-Ktmnetsov方程，得到了它的近似周期解。该解与精确解符合很好，结果表明，同伦分析法在求解高维非线性演化方程时，仍然是一种行之有效的方法。同时，还对该方法进行了一定的扩展，经过扩展后的方法能够更方便地求解更多非线性演化方程的高精度近似解析解。

英文摘要：

We obtained 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 got 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 analytical solutions for more nonlinear evolution equations in an easier way.