In this study, the (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyama equation arising from the (3 + 1)-dimensional Kadomtsev–Petviashvili equation is investigated in detail by using two powerful approaches. First, the generalized resonant multi-soliton solution is generated via the simplified linear superposition principle. Second, after applying the simplest equation method, the generalized single solitary solution is extracted. The results show that the obtained solutions are perfect. The physical explanation of the obtained solutions is depicted in various 3D and 2D figures, which are used to illustrate that the interactions of resonant multi-soliton waves are inelastic. Ultimately, the study reveals that the inelastic interactions can be determined by the sign of the wave related number ki.

中文翻译：

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(3 + 1) 维势-YTSF 方程的新孤子和共振多孤子解

在这项研究中，通过使用两种强大的方法详细研究了由 (3 + 1) 维 Kadomtsev-Petviashvili 方程产生的 (3 + 1) 维势-Yu-Toda-Sasa-Fukuyama 方程。首先，通过简化的线性叠加原理生成广义谐振多孤子解。其次，应用最简单方程法，提取广义单孤解。结果表明，得到的解决方案是完美的。所获得解决方案的物理解释在各种 3D 和 2D 图中进行了描述，用于说明共振多孤子波的相互作用是非弹性的。最终，该研究表明，非弹性相互作用可以通过波相关数的符号来确定ķ一世.