In this paper, a new (3+1)-dimensional nonlinear evolution equation is introduced, through the generalized bilinear operators based on prime number p=3. By Maple symbolic calculation, one-, two-lump, and breather-type periodic soliton solutions are obtained, where the condition of positiveness and analyticity of the lump solution are considered. The interaction solutions between the lump and multi-kink soliton, and the interaction between the lump and breather-type periodic soliton are derived, by combining multi-exponential function or trigonometric sine and cosine functions with a quadratic one. In addition, new interaction solutions between a lump, periodic-solitary waves, and one-, two- or even three-kink solitons are constructed by using the ansatz technique. Finally, the characteristics of these various solutions are exhibited and illustrated graphically.

通过基于质数p的广义双线性算子，引入了新的（3 + 1）维非线性发展方程= 3。通过Maple符号计算，得到一，二，呼吸形式的周期孤子解，其中考虑了该块解的正性和解析性条件。通过将多指数函数或三角正弦和余弦函数与二次函数相结合，得出块与多纠缠孤子之间的相互作用解以及块与呼吸型周期性孤子之间的相互作用。另外，通过使用ansatz技术构造了一个整体，周期性孤波与一种，两种或什至三种扭索孤子之间的新的相互作用解决方案。最后，这些各种解决方案的特性将以图形方式展示和说明。