Unraveling dynamics: Analytical insights into liquid-gas interactions

This study employs analytical and semi -analytical methodologies to investigate the dynamic behavior of a (3+1)-dimensional nonlinear model representing the intricate interactions between a liquid and gas bubbles. The utilization of advanced techniques, including the Khater II method, Bernoulli sub -equation function approach, and Adomian decomposition method, facilitates the derivation of novel solitary and periodic wave solutions. These solutions provide crucial insights into the fundamental physical principles governing complex phenomena such as bubble formation, growth, deformation, and collapse. The investigated (3+1) -dimensional nonlinear model serves as a comprehensive mathematical representation, capturing the interplay between dispersion, convection, diffusion, and nonlinearity - effects that play pivotal roles in the dynamics of bubbly liquid systems. The obtained solitary wave solutions contribute to unraveling the underlying mechanisms that dictate bubble evolution and interactions, thereby enhancing theoretical comprehension of these intricate processes. The analytical treatment of this model holds significant implications for various applications, spanning industrial processes, biomedical imaging and therapy, naval engineering, and environmental studies. By analytically deriving solutions for this intricate system, the study advances the understanding of bubble dynamics, offering potential avenues for optimized control and design of systems involving bubble formation and behavior. Moreover, the implementation of the Adomian decomposition technique presents an alternative avenue for uncovering additional solutions, further enriching the analytical toolkit for addressing nonlinear bubble dynamics models. The rigorous verification of solution accuracy, stability analysis, and graphical representations provide a multifaceted perspective, reinforcing the physical relevance and robustness of the obtained results. In essence, this research contributes to the broader fields of nonlinear sciences, fluid dynamics, and analytical approaches for differential equations by offering novel insights into the mathematical intricacies and physical interpretations of a (3+1) -dimensional nonlinear model governing bubble dynamics in liquids.