Qualitative analysis, exact solutions and symmetry reduction for a generalized (2＋1)-dimensional KP–MEW-Burgers equation

• Published in: Chaos, solitons and fractals solitons and fractals, 2024-04, Vol.181, p.114647, Article 114647
• Main Authors: Rafiq, Muhammad Hamza, Raza, Nauman, Jhangeer, Adil, Zidan, Ahmed M.
• Format: Article
• Language: English
• Subjects: Bifurcation and chaos theory; Generalized KP–MEW-Burgers equation; Qualitative analysis of dynamical systems; Solitary waves; Symmetry reduction
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2024.114647

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. •Application of the generalized logistic equation method to address the dynamics of solitary wave solutions for the generalized KP–MEW-Burgers equation.•Computation of the invariant transformations and symmetry reductions using Lie symmetry analysis.•Bifurcation and phase portraits of the unperturbed dynamical system using the idea of bifurcation theory of dynamical systems.•Chaos behavior of the perturbed dynamical system is identified through different chaos detecting tools using chaos theory of dynamical systems.