English

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

Analysis of PDEs 2012-11-29 v1 Spectral Theory Exactly Solvable and Integrable Systems

Abstract

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.

Keywords

Cite

@article{arxiv.1107.1982,
  title  = {KdV equation in the quarter--plane: evolution of the Weyl functions and unbounded solutions},
  author = {Alexander Sakhnovich},
  journal= {arXiv preprint arXiv:1107.1982},
  year   = {2012}
}