The aim of this study is to explore some semi-domain soliton solutions for the fractal (3+1)-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation (GKPBe) within He’s fractal derivative. First, the fractal soliton molecules are plumbed by combining the Hirota equation and fractal two-scale transform. Second, the Bernoulli sub-equation function approach together with the fractal two-scale transform is employed to investigate the other soliton solutions, which include the kink soliton and the rough wave soliton solutions. The impact of the different fractal orders on the physical behaviors of the semi-domain soliton solutions is also discussed graphically. The methods mentioned in this research are expected to provide some new viewpoints on the behaviors of the fractal PDEs.

本研究的目的是探索 He 分形导数内分形 (3+1) 维广义 Kadomtsev-Petviashvili-Boussinesq 方程 (GKPBe) 的一些半域孤子解。首先，结合Hirota方程和分形二尺度变换来探查分形孤子分子。其次，采用伯努利子方程函数方法和分形二尺度变换来研究其他孤子解，包括扭结孤子解和粗糙波孤子解。还以图形方式讨论了不同分形阶数对半域孤子解的物理行为的影响。本研究中提到的方法有望为分形偏微分方程的行为提供一些新的观点。