Abstract

. Recursion operators of partial differential equations are identified with Backlund auto-transformations of linearized diffieties. 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 infinite families of symmetries (Olver [13]). Standard reference is [14]. The presence of a recursion operator has been soon recognized as one of the attributes of the complete integrability. An exact and rich theory has been developed within the class of evolution equations (see Fokas [2] and references therein). Recursion operators are, as a rule, nonlocal and so may turn out to be the symmetries they generate (giving a powerful source of nonlocal symmetries [10, 5]). A remarkable problem of inverting a recursion operator motivated Guthrie [3] to a generalization, with consequences for generation of n...

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