For power-law nonlinear system in higher-dimensional setting like the three-dimensional case, we derived its bright soliton solution with specific power-law feature based on the self-similar method. The dynamical evolution pattern of the derived solution is pictorially demonstrated which illustrates the typical bright soliton feature. The theoretical results presented in this work can be used to guide experimental observation of soliton behavior in higher-dimensional system with power-law nonlinearity.

中文翻译：

---

具有幂律非线性的高维系统中的亮孤子动力学

对于三维情况下的高维幂律非线性系统，我们基于自相似方法推导出了具有特定幂律特征的亮孤子解。导出解的动态演化模式以图形方式展示，说明了典型的亮孤子特征。这项工作中提出的理论结果可用于指导具有幂律非线性的高维系统中孤子行为的实验观察。