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By means of the classical method, we investigate the (3+1)-dimensional Zakharov--Kuznetsov equation. The symmetry group of the (3+1)-dimensional Zakharov--Kuznetsov equation is studied first and the theorem of group invariant solutions is constructed. Then using the associated vector fields of the obtained symmetry, we give the one-, two-, and three-parameter optimal systems of group-invariant solutions. Based on the optimal system, we derive the reductions and some new solutions of the (3+1)-dimensional Zakharov--Kuznetsov equation. 相似文献
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