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From Nothing to Something: Discrete Integrable Systems |
| LOU Sen-Yue1,2**, LI Yu-Qi1,2, TANG Xiao-Yan3 |
1Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062
2Faculty of Science, Ningbo University, Ningbo 315211
3Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240
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| Cite this article: |
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LOU Sen-Yue, LI Yu-Qi, TANG Xiao-Yan 2013 Chin. Phys. Lett. 30 080202 |
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Abstract Chinese ancient sage Laozi said that everything comes from 'nothing'. Einstein believes the principle of nature is simple. Quantum physics proves that the world is discrete. And computer science takes continuous systems as discrete ones. This report is devoted to deriving a number of discrete models, including well-known integrable systems such as the KdV, KP, Toda, BKP, CKP, and special Viallet equations, from 'nothing' via simple principles. It is conjectured that the discrete models generated from nothing may be integrable because they are identities of simple algebra, model-independent nonlinear superpositions of a trivial integrable system (Riccati equation), index homogeneous decompositions of the simplest geometric theorem (the angle bisector theorem), as well as the M?bious transformation invariants.
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Received: 11 April 2013
Published: 21 November 2013
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| PACS: |
02.30.Ik
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(Integrable systems)
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02.90.+p
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(Other topics in mathematical methods in physics)
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02.30.Jr
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(Partial differential equations)
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