Kac-Moody groups and integrability of soliton equations.
KAM techniques in PDE
KAM theory for the hamiltonian derivative wave equation
We prove an infinite dimensional KAM theorem which implies the existence of Cantor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations.
Kink solutions of the binormal flow
I shall present some recent work in collaboration with S. Gutierrez on the characterization of all selfsimilar solutions of the binormal flow : which preserve the length parametrization. Above is a curve in , the arclength parameter, and denote the temporal variable. This flow appeared for the first time in the work of Da Rios (1906) as a crude approximation to the evolution of a vortex filament under Euler equation, and it is intimately related to the focusing cubic nonlinear Schrödinger...
KP trigonometric solitons and an adelic flag manifold.