Unresolved problems in the theory of integrable systems
Appears in collection : French-American conference on nonlinear dispersive PDEs / Conférence franco-américaine sur les EDP dispersives non linéaires
In spite of enormous success of the theory of integrable systems, at least three important problems are not resolved yet or are resolved only partly. They are the following: 1. The IST in the case of arbitrary bounded initial data. 2. The statistical description of the systems integrable by the IST. Albeit, the development of the theory of integrable turbulence. 3. Integrability of the deep water equations. These three problems will be discussed in the talk.
