| Issue |
Math. Model. Nat. Phenom.
Volume 7, Number 2, 2012
Solitary waves
|
|
|---|---|---|
| Page(s) | 131 - 145 | |
| DOI | https://doi.org/10.1051/mmnp/20127211 | |
| Published online | 29 February 2012 | |
KdV Equation in the Quarter–Plane: Evolution of the Weyl Functions and Unbounded Solutions
Department of Mathematics, University of Vienna,
Nordbergstrasse 15,
A-1090
Vienna,
Austria
⋆ Corresponding author. E-mail: Oleksandr.Sakhnovych@univie.ac.at
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.
Mathematics Subject Classification: 35Q53 / 34B20 / 35G31
Key words: KdV / initial–boundary value problem / Weyl function / evolution / low–energy asymptotics / blow–up solution
© EDP Sciences, 2012
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.