Under investigation in this paper is a (3+1)-dimensional nonlinear evolution equation, which was proposed and analyzed to study features and properties of nonlinear dynamics in higher dimensions. Using the Hirota bilinear method, we construct a bilinear Bäcklund transformation, which consists of four equations and involves six free parameters. With test function method and symbolic computation, three sets of lump–kink solutions and new types of interaction solutions are derived, and figures are presented to reveal the interaction behaviors. Setting constraints to the new interaction solution via the test function expressed by “polynomial-cos-cosh,” we simulate the periodic interaction phenomenon. Pfaffian solutions to the (3+1)-dimensional nonlinear evolution equation are obtained based on a set of linear partial differential conditions. According to our results, the diversity of solutions to the (3+1)-dimensional nonlinear evolution equation is revealed.

本文研究的是一个（3+1）维非线性演化方程，该方程被提出并分析以研究更高维非线性动力学的特征和性质。使用 Hirota 双线性方法，我们构建了一个双线性 Bäcklund 变换，它由四个方程组成，涉及六个自由参数。通过测试函数法和符号计算，推导出三组块扭结解和新型交互解，并用图形来揭示交互行为。通过“polynomial-cos-cosh”表示的测试函数对新的交互解决方案设置约束，我们模拟了周期性交互现象。(3+1) 维非线性演化方程的 Pfaffian 解是基于一组线性偏微分条件获得的。