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The Bargmann symmetry constraint and binary nonlinearization of the super Dirac systems

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Abstract

An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Dirac systems. Under the obtained symmetry constraint, the n-th flow of the super Dirac hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold R 4N|2N with the corresponding dynamical variables x and t n . The integrals of motion required for Liouville integrability are explicitly given.

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Authors and Affiliations

  1. School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China

    Jing Yu

  2. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, China

    Jing Yu, Jingsong He & Yi Cheng

  3. Department of Mathematics, Ningbo University, Ningbo, 315211, Zhejiang, China

    Jingsong He

  4. Department of Mathematics and Statistics, University of South Florida, Florida, 33620-5700, USA

    Wenxiu Ma

Authors
  1. Jing Yu
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  2. Jingsong He
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  3. Wenxiu Ma
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  4. Yi Cheng
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Correspondence to Jing Yu.

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Project supported by the Hangdian Foundation (No. KYS075608072), the National Natural Science Foundation of China (Nos. 10671187, 10971109) and the Program for New Century Excellent Talents in University of China (No. NCET-08-0515).

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Yu, J., He, J., Ma, W. et al. The Bargmann symmetry constraint and binary nonlinearization of the super Dirac systems. Chin. Ann. Math. Ser. B 31, 361–372 (2010). https://doi.org/10.1007/s11401-009-0032-6

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  • DOI: https://doi.org/10.1007/s11401-009-0032-6

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