By: Davide Masoero
From: Universidade de Lisboa
At: Instituto de Investigação Interdisciplinar, Anfiteatro
In some strongly nonlinear regime, solutions ofÂ PDEs undergo a phase transition from a regular to a highly-oscillatory behaviour.
The transition should be universal and exactly described by some known special functions, called Painleve transcendents. I will introduce this recent field of research focusing on one particular example, the semiclassical limit of the Korteweg-de Vries (KdV) equation.
With the help of the audience, I will try to elucidate the similarity between the theory of universality for PDEs and the analogous and celebrated theory for second order phase transitions of statistical mechanics.