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