2018-08-012024-05-17https://scholars.lib.ntu.edu.tw/handle/123456789/670910Abstract: Our aim in this project is to study the dynamics of dispersive waves for model equations such as Green-Naghdi equations and its variant arising from the shallow water theory and the related problems. We will investigate a novel approach that combines techniques from numerical methods for partial differential equations and optimization methods (such as $l_{1}$-type algorithm) in information sciences for the analysis of solutions; this is different from the classical approach that is based on the Whitham`s modulation theory, and will be more efficient than performing direct numerical simulation using the full set of equations. Dispersive waves arise in many field of sciences and technology. The development of efficient tools to analyze the dynamics of dispersive waves is of fundamental importance for practical applications.Gas-liquid bubbly flowdispersive shock waveIordanski-Kogarko-Wijngaarden modelhigh order method