In the present paper, some new exact solutions of the (3+1)-dimensional sinh-Gorden equation are displayed. First, based on the Lie point symmetry, basic infinitesimal generators given; also, and the Lie algebra and commutative relations are shown. Second, some exact solutions are obtained using the F-expansion method, and a great many Jacobian-elliptic function solutions are presented. Finally, other forms of solutions are derived using the traveling wave transform.

中文翻译：

---

新的 (3+1) 维 sinh-Gorden 方程的对称性和新精确解

在本文中，显示了 (3+1) 维 sinh-Gorden 方程的一些新精确解。首先，基于李点对称性，给出基本的无穷小发生器；此外，还显示了李代数和交换关系。其次，利用F展开法得到了一些精确解，并给出了大量的雅可比椭圆函数解。最后，使用行波变换推导出其他形式的解。