Time-Dependent Recursion Operators and Symmetries

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/).

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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  -