Qualitative Analysis and Traveling Wave Solutions of a (3 + 1)- Dimensional Generalized Nonlinear Konopelchenko-Dubrovsky-Kaup-Kupershmidt System

This article investigates the qualitative analysis and traveling wave solutions of a (3 + 1)-dimensional generalized nonlinear Konopelchenko-Dubrovsky-Kaup-Kupershmidt system. This equation is commonly used to simulate nonlinear wave problems in the fields of fluid mechanics, plasma physics, and nonlinear optics, as well as to transform nonlinear partial differential equations into nonlinear ordinary differential equations through wave transformations. Based on the analysis of planar dynamical systems, a nonlinear ordinary differential equation is transformed into a two-dimensional dynamical system, and the qualitative behavior of the two-dimensional dynamical system and its periodic disturbance system is studied. A two-dimensional phase portrait, three-dimensional phase portrait, sensitivity analysis diagrams, Poincaré section diagrams, and Lyapunov exponent diagrams are provided to illustrate the dynamic behavior of two-dimensional dynamical systems with disturbances. The traveling wave solution of a Konopelchenko-Dubrovsky-Kaup-Kupershmidt system is studied based on the complete discriminant system method, and its three-dimensional, two-dimensional graphs and contour plots are plotted. These works can provide a deeper understanding of the dynamic behavior of Konopelchenko-Dubrovsky-Kaup-Kupershmidt systems and the propagation process of waves.