On the Transformations of Symplectic Expansions and the Respective Bäcklund Transformation for the KDV Equation

Khristov, E.. "On the Transformations of Symplectic Expansions and the Respective Bäcklund Transformation for the KDV Equation." Serdica Mathematical Journal 29.1 (2003): 75-94. <http://eudml.org/doc/219578>.

@article{Khristov2003,
abstract = {2000 Mathematics Subject Classification: Primary: 34B40; secondary: 35Q51, 35Q53By using the Deift–Trubowitz transformations for adding or removing bound states to the spectrum of the Schrödinger operator on the line we construct a simple algorithm allowing one to reduce the problem of deriving symplectic expansions to its simplest case when the spectrum is purely continuous, and vice versa. We also obtain the transformation formulas for the correponding recursion operator. As an illustration of this approach, the Bäcklund transformations for the KdV equation are constructed.This work is partially supported by Bulgarian NFSR Grant MM 810/98 and Grant 361/01 of Sofia University “St Kl. Ohridski”.},
author = {Khristov, E.},
journal = {Serdica Mathematical Journal},
keywords = {Symplectic Expantion; KdV Equation; Bäcklund Transformation; Deift-Trubowitz transformation},
language = {eng},
number = {1},
pages = {75-94},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {On the Transformations of Symplectic Expansions and the Respective Bäcklund Transformation for the KDV Equation},
url = {http://eudml.org/doc/219578},
volume = {29},
year = {2003},
}

TY - JOUR
AU - Khristov, E.
TI - On the Transformations of Symplectic Expansions and the Respective Bäcklund Transformation for the KDV Equation
JO - Serdica Mathematical Journal
PY - 2003
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 29
IS - 1
SP - 75
EP - 94
AB - 2000 Mathematics Subject Classification: Primary: 34B40; secondary: 35Q51, 35Q53By using the Deift–Trubowitz transformations for adding or removing bound states to the spectrum of the Schrödinger operator on the line we construct a simple algorithm allowing one to reduce the problem of deriving symplectic expansions to its simplest case when the spectrum is purely continuous, and vice versa. We also obtain the transformation formulas for the correponding recursion operator. As an illustration of this approach, the Bäcklund transformations for the KdV equation are constructed.This work is partially supported by Bulgarian NFSR Grant MM 810/98 and Grant 361/01 of Sofia University “St Kl. Ohridski”.
LA - eng
KW - Symplectic Expantion; KdV Equation; Bäcklund Transformation; Deift-Trubowitz transformation
UR - http://eudml.org/doc/219578
ER -