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KdV Equation in the Quarter–Plane: Evolution of the WeylFunctions and Unbounded Solutions

Published online by Cambridge University Press:  29 February 2012

A. Sakhnovich
A. Sakhnovich*
Affiliation:
Department of Mathematics, University of Vienna, Nordbergstrasse 15, A-1090 Vienna, Austria
*
⋆ Corresponding author. E-mail: Oleksandr.Sakhnovych@univie.ac.at
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Abstract

The matrix KdV equation with a negative dispersion term is considered in the right upperquarter–plane. The evolution law is derived for the Weyl function of a correspondingauxiliary linear system. Using the low energy asymptotics of the Weyl functions, theunboundedness of solutions is obtained for some classes of the initial–boundaryconditions.

Keywords

KdVinitial–boundary value problemWeyl functionevolutionlow–energy asymptoticsblow–up solution
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 2: Solitary waves , 2012 , pp. 131 - 145
Copyright
© EDP Sciences, 2012

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