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}
}