k-component disconjugacy for systems of ordinary differential equations.
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.