Anthony Thomas Lyons (26/03/18)

Anders Claesson, mars 22, 2018

Málstofa í stærðfræði

Fyrirlesari: Anthony Thomas Lyons, Waterford Institute of Technology

Titill: The dressing method for the Camassa-Holm equation

Staðsetning: HB-5 (Háskólabíó)
Tími: Mánudagur 26. mars kl. 10:50

Ágrip:

The Camassa-Holm equation is a nonlinear shallow water model which has been the focus of a great deal of mathematical research in hydrodynamics for the past two decades. This interest is in part due to the versatility of the system, being relevant as a fluid model possessing solutions which display wave-breaking along with global solutions in the form of soliton, peakon and cuspon solutions.
The inverse scattering transform has been successfully implemented to construct numerous global solutions of this system, and in this talk we present a recently developed variation of this method for the Camassa-Holm equation, known as the dressing method. This efficient implementation allows one to integrate several nonlinear hydrodynamical models, and in particular we shall outline the details of this new dressing method and use it to construct the one and two-soliton solutions of the Camassa-Holm equation.