Abstract
We consider integrable hierarchies of evolution equations defined with the help of the hereditary recursion operator which is related to the auxiliary second-order linear eigenvalue problem with energy-dependent potential. Explicit formulae of symmetry transformations generated by the shift of the spectral parameter, , are derived. We refer to such transformations as Galilei-type ones this because particular case is the well known Galilei transformation for the Korteweg-de Vries (KdV) equation. We apply a symmetry method for simultaneous construction of the invariant solution of the first two members of the KdV hierarchy.
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