Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan.
Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan.
PLoS One. 2024 Aug 27;19(8):e0305094. doi: 10.1371/journal.pone.0305094. eCollection 2024.
This study endeavors to examine the dynamics of the generalized Kadomtsev-Petviashvili (gKP) equation in (n + 1) dimensions. Based on the comprehensive three-wave methodology and the Hirota's bilinear technique, the gKP equation is meticulously examined. By means of symbolic computation, a number of three-wave solutions are derived. Applying the Lie symmetry approach to the governing equation enables the determination of symmetry reduction, which aids in the reduction of the dimensionality of the said equation. Using symmetry reduction, we obtain the second order differential equation. By means of applying symmetry reduction, the second order differential equation is derived. The second order differential equation undergoes Galilean transformation to obtain a system of first order differential equations. The present study presents an analysis of bifurcation and sensitivity for a given dynamical system. Additionally, when an external force impacts the underlying dynamic system, its behavior resembles quasi-periodic phenomena. The presence of quasi-periodic patterns are identified using chaos detecting tools. These findings represent a novel contribution to the studied equation and significantly advance our understanding of dynamics in nonlinear wave models.
本研究致力于研究（n + 1）维广义 Kadomtsev-Petviashvili（gKP）方程的动力学。基于全面的三波方法和 Hirota 的双线性技术，对 gKP 方程进行了细致的研究。通过符号计算，得到了一些三波解。利用支配方程的李对称方法可以确定对称约化，这有助于降低方程的维数。通过对称约化，我们得到了二阶微分方程。通过应用对称约化，推导出二阶微分方程。二阶微分方程经历伽利略变换，得到一个一阶微分方程组。本研究对给定的动力系统进行了分叉和敏感性分析。此外，当外部力作用于基础动力系统时，其行为类似于准周期现象。使用混沌检测工具来识别准周期模式的存在。这些发现代表了对所研究方程的新贡献，极大地提高了我们对非线性波模型动力学的理解。
