KdV equation in the quarter--plane: evolution of the Weyl functions and unbounded solutions

Details KdV equation in the quarter--plane: evolution of the Weyl functions and unbounded solutions KdV equation in the quarter--plane: evolution of the Weyl functions and unbounded solutions

2011-07-11

arxiv.org/abs/1107.1982v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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