The objective of this manuscript is to examine the non-linear characteristics of the modified equal width-Burgers equation, known as the generalized Kadomtsive–Petviashvili equation, and its ability to generate a long-wave with dispersion and dissipation in a nonlinear medium. We employ the Lie symmetry approach to reduce the dimension of the equation, resulting in an ordinary differential equation. Utilizing the newly developed generalized logistic equation method, we are able to derive solitary wave solutions for the aforementioned ordinary differential equation. In order to gain a deeper understanding of the physical implications of these solutions, we present them using various visual representations, such as 3D, 2D, density, and polar plots. Following this, we conduct a qualitative analysis of the dynamical systems and explore their chaotic behavior using bifurcation and chaos theory. To identify chaos within the systems, we utilize various chaos detection tools available in the existing literature. The results obtained from this study are novel and valuable for further investigation of the equation, providing guidance for future researchers.

中文翻译：

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广义(2+1)维KP–MEW-Burgers方程的定性分析、精确解和对称性约简

本手稿的目的是检查修改后的等宽伯格斯方程（称为广义 Kadomtsive-Petviashvili 方程）的非线性特性，及其在非线性介质中产生具有色散和耗散的长波的能力。我们采用李对称方法来降低方程的维数，从而得到一个常微分方程。利用新开发的广义逻辑方程方法，我们能够推导上述常微分方程的孤立波解。为了更深入地了解这些解决方案的物理含义，我们使用各种视觉表示形式（例如 3D、2D、密度图和极坐标图）来呈现它们。接下来，我们对动力系统进行定性分析，并利用分岔和混沌理论探索其混沌行为。为了识别系统内的混沌，我们利用现有文献中提供的各种混沌检测工具。这项研究获得的结果是新颖的，对于进一步研究该方程很有价值，为未来的研究人员提供指导。