KdV equation in the quarter-plane: evolution of the Weyl functions and unbounded solutions. (English) Zbl 1251.35137
Summary: 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.
MSC:
35Q53 | KdV equations (Korteweg-de Vries equations) |
34B20 | Weyl theory and its generalizations for ordinary differential equations |
35G31 | Initial-boundary value problems for nonlinear higher-order PDEs |