S Y Lou, Yu-qi Li, Xiao-yan Tang
Chinese ancient sage Laozi said `\emph{Dao sheng yi, yi sheng er, er sheng
san, san sheng wanwu}, ...' that means something even everything comes from
\emph{\bf \em `nothing'} via `\bf \em Dao'. \rm In this paper, various discrete
integrable models, including the known discrete Schwarzian KdV, KP, BKP, CKP,
special Viallet equations and many other unknowns are derived from nothing. The
ancient Greek geometric theorems, such as the angle bisector theorem, are also
closely related to the discrete integrable models. It is conjectured that all
the discrete models generated from nothing may be integrable, because they are
identities of a same algebra, model independent nonlinear superpositions of the
Riccati equations, index homogeneous decompositions of the angle bisector
theorem and M\"obious transformation invariants.
View original:
http://arxiv.org/abs/1201.5924
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