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

Mathematical Modelling of Natural Phenomena (2012)

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

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topSakhnovich, 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 -

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