中文摘要：

应用微分方程动力系统定性理论,讨论（3＋1）维ZK方程的鞍-鞍行波同（异）宿轨和周期闭轨的存在性.运用椭圆方程映射法求得方程的精确孤波解、冲击波解和周期波解。

英文摘要：

In this paper,based on the qualitative analysis theory of differential equations,we discuss the existence of the saddlesaddle traveling wave with same （different） periodic orbits and the existence of the periodic closed orbits for the （3 ＋ 1）-dimensional ZK equation.Moreover,by using the elliptic equation mapping method,the solitary wave,shock wave and periodic wave solutions of this equation are obtained.