Peakonomics, or how peaked solitons helped me to understand the economy

Abstract: The economist Paul Krugman was awarded the Nobel prize for his work in economic geography. In his book "The Self-Organizing Economy" he promotes a Santa Fe-style approach to modelling complex economic systems. Krugman's arguments are illustrated with some simple mathematical models. In this talk, I explain how one such model has exact solutions with very similar properties to the peaked solitons ("peakons") that appearing in an integrable partial differential derived by Camassa and Holm in shallow water theory. The exact solutions in Krugman's integro-differential model turn out explain the numerical behaviour he observed. This is joint work with J. Kelsey and F. Medda.