Journal of Nonlinear Mathematical Physics

Volume 9, Issue 2, May 2002, Pages 210 - 228

Time-Dependent Recursion Operators and Symmetries

Authors
M. Gürses, A. Karasu, R. Turhan
Corresponding Author
M. Gürses
Received 18 November 2001, Revised 7 December 2001, Accepted 1 January 2002, Available Online 1 May 2002.
DOI
10.2991/jnmp.2002.9.2.5How to use a DOI?
Abstract

The recursion operators and symmetries of nonautonomous, (1 + 1) dimensional itegrable evolution equations are considered. It has been previously observed that the symmetries of the integrable evolution equations obtained through their recursion oerators do not satisfy the symmetry equations. There have been several attempts to resolve this problem. It is shown that in the case of time-dependent evolution equtions or time-dependent recursion operators associativity is lost. Due to this fact such recursion operators need modification. A general formula is given for the missing term of the recursion operators. Apart from the recursion operators a method is introduced to calculate the correct symmetries. For illustrations several examples of scalar and coupled system of equations are considered.

Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
9 - 2
Pages
210 - 228
Publication Date
2002/05/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2002.9.2.5How to use a DOI?
Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - M. Gürses
AU  - A. Karasu
AU  - R. Turhan
PY  - 2002
DA  - 2002/05/01
TI  - Time-Dependent Recursion Operators and Symmetries
JO  - Journal of Nonlinear Mathematical Physics
SP  - 210
EP  - 228
VL  - 9
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2002.9.2.5
DO  - 10.2991/jnmp.2002.9.2.5
ID  - Gürses2002
ER  -