Abstract
The bi-Hamiltonian structure of integrable supersymmetric extensions of the Korteweg-de Vries (KdV) equation related to theN=1 and theN=2 superconformal algebras is found. It turns out that some of these extensions admit inverse Hamiltonian formulations in terms of presymplectic operators rather than in terms of Poisson tensors. For one extension related to theN=2 case additional symmtries are found with bosonic parts that cannot be reduced to symmetries of the classical KdV. They can be explained by a factorization of the corresponding Lax operator. All the bi-Hamiltonian formulations are derived in a systematic way from the Lax operators.
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Communicated by H. Araki
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Oevel, W., Popowicz, Z. The bi-Hamiltonian structure of fully supersymmetric Korteweg-de Vries systems. Commun.Math. Phys. 139, 441–460 (1991). https://doi.org/10.1007/BF02101874
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DOI: https://doi.org/10.1007/BF02101874