Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2001-08-05
J.Nonlin.Mathematical Phys.9:210-228,2002
Nonlinear Sciences
Exactly Solvable and Integrable Systems
arxiv version is already official
Scientific paper
The recursion operators and symmetries of non-autonomous, (1+1)-dimensional integrable evolution equations are considered. It has been previously observed that the symmetries of the integrable evolution equations obtained through their recursion operators 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 equations or time dependent recursion operators, associativity is lost. Due to this fact such recursion operators need modifications. 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.
Gurses Metin
Karasu Atalay
Turhan Refik
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