Stability and instability for the fractional KdV equation in all spatial dimensions

Speaker: Oscar Riaño

Universidad Nacional de Colombia, Bogotá

Date: Monday, November 27th, 2023 at 12 Santiago time

Abstract: We will study the fractional Korteweg-de Vries equation (fKdV) in several spatial dimensions. This is a nonlinear dispersive model where dispersive effects are studied through the fractional Laplacian. The equation appears in contexts such as water waves, waves in stratified fluids, boundary-layer type shear flow, and ion-acoustic waves, among others.

We will focus on traveling wave solutions (or solitary waves) of fKdV and analyze questions of orbital stability/instability of such solutions. We will see that our results are valid for arbitrary dimen- sions, thus we recover and establish new results for the most studied case the one-dimensional fKdV.

Joint work with Svetlana Roudenko (Florida International University (FIU)).

Venue:  Sala de Seminarios, 5th floor, Beauchef 851 / Online via Zoom
Chair: Ricardo Freire