AI 中文总结
本研究针对（2+1）维七阶sCDG-KP方程，采用（$\frac{G^{\text{'}}}{G^{\text{'}}+G+A}$）方法求解精确解，通过分岔等分析揭示其混沌结构等动力学特性，为该类非线性方程的研究提供了图形化支撑。
AI 中文摘要
本研究的主要目标是探究（2+1）维七阶Caudrey-Dodd-Gibbon-KP（sCDG-KP）方程的行波解与动力学特性。应用（$\frac{G^{\text{'}}}{G^{\text{'}}+G+A}$）方法，通过合适的波变换将（2+1）维七阶Caudrey-Dodd-Gibbon-KP（sCDG-KP）方程转化为简化常微分方程（ODE），进而求解其精确解。为便于理解所得解的实际应用价值，提供了已确定解的二维、三维及热图等图形表示。最终获得了亮孤子解与反扭结孤子解。随后，将该常微分方程转化为二维方程组，通过分岔分析、相图与吸引子分析探究简化系统的动力学行为，过程中绘制了分岔相图、二维相图、三维相图、时间序列、混沌吸引子、敏感性分析、分形维数、递归图及动力学系统的功率谱等可视化图形。
英文摘要
The main objective of this work is to investigate the traveling wave solution and dynamic characteristics of the (2 + 1)-dimensional seventh-order Caudrey-Dodd-Gibbon-KP (sCDG-KP) equation. Applying the ($\frac{G^{\prime}}{G^{\prime}+G+A}$) method, we examine the exact solution of the (2 + 1)-dimensional seventh-order Caudrey-Dodd-Gibbon-KP (sCDG-KP) equation by altering it into a reduced ODE via a suitable wave transformation. Graphical representations, such as 2D, 3D, and a heat map of the ascertained solution, are present to facilitate comprehension of the empirical relevance of the obtained solutions. As a result, we acquired a bright and anti-kink soliton solution. Next, we alter the ODE into a 2D system of equations to analyze the dynamical behavior of the reduced system via bifurcation analysis, phase portrait, and attractor analysis. During this process, we portray the graphical visualization of the bifurcation phase portrait, 2D phase portrait, 3D phase portrait, time series, chaotic attractor, sensitive analysis, fractal dimension, recurrence plot, and power spectrum of the dynamical system.
