Skip to Main Content

Applied Math Seminar: Numerical studies of the Davey-Stewartson and Zakharov-Kuznetsov equations by Nikola Stoilov

This is a past event.

Friday, May 21, 2021 at 10:00am

Virtual Event

Speaker: Nikola Stoilov, University of Bourgogne, Dijon (France)

Title: Numerical studies of the Davey-Stewartson and Zakharov-Kuznetsov equations

Abstract: In this work we look at the behaviour of the Davey-Stewartson (DS) and Zakharov Kuznetsov (ZK) equations, using advanced numerical tools. As a nonlinear dispersive PDE and a generalization of the non-linear Schrödinger equation, DS has explicit solutions that develop a singularity in finite time. We will discuss the long time behaviour and potential blow-up of solutions to the focusing Davey-Stewartson II equation for various initial data and propose a conjecture describing the rate and solution profiles near the singularity. We will also look at integrable properties of DS and the associated scattering problem. ZK is also a nonlinear dispersive PDE and can be seen as a generalisation of the KdV, however it is not integrable. We demonstrate its behaviour as a dispersive PDE and will look at blow-up, soliton resolution and soliton interaction and discuss how the non-integrability transpires in these cases. We propose several conjectures for the long term behaviour.

Based on joint works with Christian Klein and Ken McLaughlin and Svetlana Roudenko.

Zoom Link: https://fiu.zoom.us/j/94146267582?pwd=SWpaZHFmM2pZS1VXb3pNa1Uyb3hVdz09

Event Type

Academics, Lectures & conferences

Audience

Students, Faculty & Staff

Department
Department of Mathematics and Statistics
Add to Calendar
Google Calendar iCal Outlook

Recent Activity

Statement of Free Expression

FIU endorses the Florida Board of Governors' Statement of Free Expression to support and encourage full and open discourse and the robust exchange of ideas and perspectives on our campuses. In addition to supporting this legal right, we view this as an integral part of our ability to deliver a high-quality academic experience for our students, engage in meaningful and productive research, and provide valuable public service. This includes fostering civil and open dialogue in support of critical thinking in and out of the classroom, including events hosted by the university.