Ufa Mathematical Journal
    Volume 4, Number 3, pp. 104-152

    Integrable evolution equations with the constant separant.

    Meshkov A.G., Sokolov V.V.

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    The survey contains results of classification for integrable one-field evolution equations of orders 2, 3 and 5 with the constant separant. The classification is based on neccesary integrability conditions that follow from the existence of the formal recursion operator for integrable equations. Recursion formulas for the whole infinite sequence of these conditions are presented for the first time. The most of the classification statements can be found in papers by S.I. Svinilupov and V.V. Sokolov but the proofs never been published before. The result concerning the fifth order equations is stronger then obtained before.