7 research outputs found
From nothing to something: discrete integrable systems
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\"obious transformation invariants.Comment: 11 pages, side 10 repor