Discrete and continuous integrable systems possessing the same non-dynamical r-matrix |
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| Institution: | 1. CCAST (World Laboratory), P.O. Box 8730, Beijing 100080, China;2. School of Mathematical Science, Peking University, Beijing 100871, China;4. Department of Mathematics, Xuzhou Normal University, Xuzhou 221009, China;1. Scuola Normale Superiore and INFN, Piazza dei Cavalieri 7, 56126 Pisa, Italy;2. University of Geneva, Department of Theoretical Physics, 24 quai Ernest-Ansermet, 1214 Genève 4, Switzerland |
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| Abstract: | We consider two different Lax representations with the same Lax matrix in terms of 2 × 2 traceless matrices: one produces the discrete integrable symplectic mapping resulting from the well-known Toda spectral problem under the discrete Bargmann-Garnier (BG) constraint; the other generates the continuous non-linearized integrable system for the c-KdV spectra problem under the corresponding BG constraint. We are surprised to find that the two very different (one is discrete, the other continuous) integrable systems possess the same non-dynamical r-matrix. |
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