The Hamiltonian structure of the N = 2 supersymmetric GNLS hierarchy |
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| Institution: | 1. International School for Advanced Studies (SISSA/ISAS), Via Beirut 2, 34014 Trieste, Italy;2. INFN, Sezione di Trieste, Italy;3. Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Moscow Region, Russia;1. School of Mathematics and Finance, Chuzhou University, Chuzhou, 239000, China;2. Applied Mathematics Research Center, Chuzhou University, Chuzhou, 239000, China;3. Shing-Tung Yau Center of Southeast University, Southeast University, Nanjing, 210096, China |
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| Abstract: | The first two Hamiltonian structures and the recursion operator connecting all evolution systems and Hamiltonian structures of the N = 2 supersymmetric (n, m)-GNLS hierarchy are constructed in terms of N = 2 superfields in two different superfield bases with local evolution equations. Their bosonic limits are studied in detail. New local and nonlocal bosonic and fermionic integrals both for the N = 2 supersymmetric (n, m)-GNLS hierarchy and its bosonic counterparts are derived. As an example, in the n = 1, m = 1 case, the algebra and the symmetry transformations for some of them are worked out and a rich N = 4 supersymmetry structure is uncovered. |
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