Shao Chuanlin, Yang Lu, Yan Yongsheng, Wu Jingyu, Zhu Minting, Li Lingfei
School of Economics and Finance, Huaqiao University, Quanzhou, 362021, Fujian, People's Republic of China.
School of Economics and Management, Northwest University, Xi'an, 710127, Shaanxi, People's Republic of China.
Sci Rep. 2023 Sep 22;13(1):15826. doi: 10.1038/s41598-023-42845-0.
An extended (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq equation is studied in this paper to construct periodic solution, n-soliton solution and folded localized excitation. Firstly, with the help of the Hirota's bilinear method and ansatz, some periodic solutions have been derived. Secondly, taking Burgers equation as an auxiliary function, we have obtained n-soliton solution and n-shock wave. Lastly, we present a new variable separation method for (3+1)-dimensional and higher dimensional models, and use it to derive localized excitation solutions. To be specific, we have constructed various novel structures and discussed the interaction dynamics of folded solitary waves. Compared with the other methods, the variable separation solutions obtained in this paper not only directly give the analytical form of the solution u instead of its potential [Formula: see text], but also provide us a straightforward approach to construct localized excitation for higher order dimensional nonlinear partial differential equation.
本文研究了一个扩展的(3 + 1)维Kadomtsev - Petviashvili - Boussinesq方程，以构造周期解、n孤子解和折叠局域激发。首先，借助Hirota双线性方法和假设，推导了一些周期解。其次，以Burgers方程为辅助函数，得到了n孤子解和n冲击波。最后，针对(3 + 1)维及更高维模型提出了一种新的变量分离方法，并用它来推导局域激发解。具体而言，我们构造了各种新颖的结构，并讨论了折叠孤波的相互作用动力学。与其他方法相比，本文得到的变量分离解不仅直接给出了解u的解析形式，而不是其势函数[公式：见原文]，还为我们提供了一种构造高阶维非线性偏微分方程局域激发的直接方法。
