18:10 Семинар Международной лаборатории кластерной геометрии: Максим Павлов (Ningbo Universoty)

We introduce the concept "Central Darboux Equations". They are three-dimensional integrable equations. Shortly and formally we can distinguish these four equations as 3+0, 2+1, 1+2 and 0+3 equations for the same tau-function determined totally by 6 independent variables.
3+0 means "3 continuous variables";
2+1 means "2 continuous variables and 1 discrete variable";
1+2 means "1 continuous variable and 2 discrete variables";
0+3 means "3 discrete variables".

The first (3+0) equation is most simple and totally symmetric under permutation of indices of independent variables. By this reason, this equation obviously has advantage in comparison with all other known integrable systems in a three-dimensional (pure continuous) case.

The four (0+3) equation has similar quality in a pure discrete case. Two other (2+1) and (1+2) cases are intermediate.

This talk is based on: https://arxiv.org/abs/2603.05211