Project CEMAPRE internal
| Title | Dispersive Equations |
| Participants | Filipe Oliveira (Principal Investigator) |
| Summary | This project builds upon the 2023 internal project "Dispersive PDEs." Our focus is on the qualitative analysis of various nonlinear dispersive models, including the Schrödinger-Debye system, the Benney equations, the Whitham equation, the Camassa-Holm equation, and cubic and quadratic NLS systems. Particular emphasis will be placed on studying the abcd-Boussinesq system, which models two-wave approximations of the incompressible, irrotational, two-dimensional water wave equations in the shallow water regime, following the framework of Boussinesq’s original derivation. Additionally, we will explore dispersive properties of generalized Korteweg–de Vries-type equations and nonlinear wave interactions in higher-order water wave models. |