An extended Harry Dym hierarchy
نویسندگان
چکیده
Abstract An extended Harry Dym hierarchy is constructed by using eigenfunctions and adjoint eigenfunctions of the spectral problems of the Harry Dym hierarchy associated with the pseudo-differential operator L = u∂ +u0 +u1∂−1 + · · ·. The corresponding Lax presentation possesses a self-consistent source involving squared eigenfunctions. The resulting extended Harry Dym hierarchy is reduced to the Harry Dym hierarchy with self-consistent sources under the n-reduction, L = (L) 2, and the k-constrained Harry Dym hierarchy under the k-constraint, L = (L) 2 + ∑N i=1 qi∂ −1ri∂2. A few particular examples are computed, together with their Lax pairs.
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