Bifurcation Behaviors and Dynamical Characteristics of a Generalized KdV–mKdV-like System

This study carries out an in-depth and systematic bifurcation analysis on a generalized KdV–mKdV-like system, adopting qualitative dynamical systems theory to explore the nonlinear wave dynamics and asymptotic characteristics of the system. Through a detailed investigation of the system’s performance under different parameter combinations, we reveal complex wave phenomena that are closely correlated with parameter setting. A critical phase transition phenomenon is identified when the system operates under specific parametric conditions. The research results provide essential theoretical support for understanding nonlinear wave dynamics and system stability, which can be potentially applied to wave control and system performance optimization in various physical scenarios.