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 From nothing to something: discrete integrable systems


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Chinese ancient sage Laozi said everything comes from `nothing. m Einstein believes the principle of nature is simple. Quantum physics proves the world is discrete. And computer science takes continuous systems as discrete ones. This report is devoted to derive a number of discrete models, including those 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 a 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\-obious transformation invariants.



Author: S Y Lou; Yu-qi Li; Xiao-yan Tang

Source: https://archive.org/







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