Kac-Moody groups and integrability of soliton equations.
KAM techniques in PDE
KdV Equation in the Quarter–Plane: Evolution of the Weyl Functions and Unbounded Solutions
The matrix KdV equation with a negative dispersion term is considered in the right upper quarter–plane. The evolution law is derived for the Weyl function of a corresponding auxiliary linear system. Using the low energy asymptotics of the Weyl functions, the unboundedness of solutions is obtained for some classes of the initial–boundary conditions.
KP trigonometric solitons and an adelic flag manifold.
Kuramoto-Sivashinsky equation in domains with moving boundaries.