Dynamical Evolution of Soliton Parameters in the Modified Kawahara Equation via the Collective Variable Technique
摘要
This paper examines the modified Kawahara equation using the collective variable method to explore how soliton parameters evolve dynamically. A carefully chosen trial function simplifies the main equation into a set of ordinary differential equations that track the time-dependent behavior of key soliton features. The resulting system is analyzed semi-numerically with specific dispersion values and initial conditions. Graphs reveal that all collective variables undergo complex oscillations, reflecting the combined influence of higher-order dispersion and nonlinearity on soliton behavior. The model also shows dispersive-like effects, such as oscillating chirp, frequency modulation, and quadratic phase changes. Additionally, a heatmap of the correlation matrix is provided to show the relationships among variables, emphasizing the strong connections between amplitude, width, and phase parameters. Overall, this approach offers a thorough framework for investigating soliton parameter dynamics in the modified Kawahara equation, highlighting the utility of the collective variable method in capturing nonlinear wave characteristics.