On Wednesday the 5th of March 2025 at 14:30 Youssef Khalifeh from the Lebanese University in Hadat will give a seminar on the extended KDV equation for the description of the propagation of waves in weakly non-linear, weakly dispersive shallow water problems.
Youssef Khalifeh, Lebanese University, Hadat, terrà il seminario:
Title: A new Extended KDV Equation: Theoretical Study, Numerical Validation & Tsunami Application
Abstract: The KdV is one of the most widespread non-linear models, commonly used by coastal engineers, describing the propagation waves in weakly non-linear and weakly dispersive shallow water problems. Many oceanographical applications are represented by this equation such as tsunami waves. Over the last few decades, the derivation of the extended KdV equation has been studied extensively. However, these equations have rarely been derived rigorously. The first aim of this work is to give insight into their rigorous mathematical derivation, instead of only referring to it. We will present here a rigorous derivation of an extended KdV equation on the velocity. With this aim in mind, the primary research method for this paper will depend on the definition of consistency. Hence, a rigorous justification of new extended KdV equations will be provided thanks to this definition. This result provides a precise mathematical answer to a question raised by several authors in recent years, that is the verification of the extended KdV equations, derived previously, using formal methods. The second goal is to derive new linear asymptotical models of the extended KdV equation and then Boussinesq equations so that they have the same accuracy as the standard models. We solve explicitly these new linear models and numerically validate the results. An application for tsunami waves is also presented.
Il seminario si svolgerà presso la sede CNR-IAC di Roma, aula 116 al primo piano, via dei Taurini 19, 001815 Roma, in modalità mista: in presenza e in streaming
