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

Serdica Mathematical Journal (2003)

- Volume: 29, Issue: 1, page 75-94
- ISSN: 1310-6600

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topKhristov, 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 -

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