Noncommutative integrability and recursion operators
نویسندگان
چکیده
منابع مشابه
On Recursion Operators
We observe that application of a recursion operator of Burgers equation does not produce the expected symmetries. This is explained by the incorrect assumption that D−1 x Dx = 1. We then proceed to give a method to compute the symmetries using the recursion operator as a first order approximation.
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In this note I exhibit a “discrete homotopy” which joins the category of Fmanifolds to the category of Poisson–Nijenhuis manifolds, passing through the category of Frobenius manifolds.
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Recursion operators of partial diierential equations are identiied with BB acklund auto-transformations of linearized diieties. Relations to the classical concept and its recent Guthrie's generalization are discussed. Traditionally,a recursion operator of a PDE is a linear operator L acting on symmetries: if f is a symmetry then so is Lf. This provides a convenient way to generate innnite famil...
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In this paper we discuss the structure of recursion operators. We show that recursion operators of evolution equations have a nonlocal part that is determined by symmetries and cosymmetries. This enables us to compute recursion operators more systematically. Under certain conditions (which hold for all examples known to us) Nijenhuis operators are well defined, i.e., they give rise to hierarchi...
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ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2000
ISSN: 0393-0440
DOI: 10.1016/s0393-0440(00)00026-7