Florent Noisette (IMB)
Complete integrability for the KdV equation
The aim of the talk is to discuss the historic paper of Peter Lax where he first introduced the concept of complete integrability. The idea is twofold. Firstly, whenever there exist infinitely many conserved quantities for a given evolution equation, then its solitons interact nicely. Secondly, whenever there exists two conservation laws verifying some conditions for a given evolution equation, there exist an algorithmic procedure to compute infinitely many conservation laws for this equation.