Perturbation of Solitary Waves and Shock Waves with Surface Tension

Abstract

This manuscript is designed with an extensive aim to investigate solitary waves in shallow water with surface tension. The governing model is the perturbed sixth-order Boussinesq equation, which incorporates higher-order dispersion effects and perturbative terms that influence wave dynamics. The G′/G-expansion procedure is employed to systematically retrieve exact solitary wave solutions, providing a diverse set of wave structures that depend on the interplay between dispersion, nonlinearity, and perturbative effects. The study further establishes the necessary parameter constraints for the existence of such solitary waves, ensuring the physical viability of the obtained solutions. Additionally, a detailed analysis of the influence of perturbation terms on the soliton characteristics is provided, revealing novel behaviors and stability conditions that were previously unexplored. These findings contribute to a deeper understanding of wave propagation in shallow water systems, with potential applications in engineering and fluid dynamics.