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

A. Sakhnovich

Mathematical Modelling of Natural Phenomena (2012)

  • Volume: 7, Issue: 2, page 131-145
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Sakhnovich, A.. "KdV Equation in the Quarter–Plane: Evolution of the Weyl Functions and Unbounded Solutions." Mathematical Modelling of Natural Phenomena 7.2 (2012): 131-145. <http://eudml.org/doc/222228>.

@article{Sakhnovich2012,
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.},
author = {Sakhnovich, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {KdV; initial–boundary value problem; Weyl function; evolution; low–energy asymptotics; blow–up solution; initial-boundary value problem; low-energy asymptotics; blow-up solution},
language = {eng},
month = {2},
number = {2},
pages = {131-145},
publisher = {EDP Sciences},
title = {KdV Equation in the Quarter–Plane: Evolution of the Weyl Functions and Unbounded Solutions},
url = {http://eudml.org/doc/222228},
volume = {7},
year = {2012},
}

TY - JOUR
AU - Sakhnovich, A.
TI - KdV Equation in the Quarter–Plane: Evolution of the Weyl Functions and Unbounded Solutions
JO - Mathematical Modelling of Natural Phenomena
DA - 2012/2//
PB - EDP Sciences
VL - 7
IS - 2
SP - 131
EP - 145
AB - 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.
LA - eng
KW - KdV; initial–boundary value problem; Weyl function; evolution; low–energy asymptotics; blow–up solution; initial-boundary value problem; low-energy asymptotics; blow-up solution
UR - http://eudml.org/doc/222228
ER -

References

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