<p>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.</p>

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Dynamical Evolution of Soliton Parameters in the Modified Kawahara Equation via the Collective Variable Technique

  • Mamta Kapoor

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.