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. 
Alexander Sakhnovich
math.AP math.SP nlin.SI