Monday, November 27th at 12:00 hs (Santiago time) in the Sala de Seminarios (fifth floor), Beauchef 851.

Speaker: Prof. Oscar Riaño (Unal, Bogotá)

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

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)).