Speaker: Maxim Pavlov, Shandong University of Science and Technology, China

Title:  Lagrangian formulation of the Darboux system

Date and time: 29.04.2026, 17:00 (GMT +03:00)

Abstract: The classical Darboux system governing the rotation coefficients of three-dimensional metrics of diagonal curvature admits an equivalent formulation as a sixth-order partial differential equation for a scalar potential associated with the corresponding τ-function. In this talk, we show that this equation possesses a Lagrangian structure and can be interpreted as an explicit scalar representation of the generating PDE of the KP hierarchy, in the sense recently proposed by Frank Nijhoff within the Lagrangian multiform framework. We further construct scalar Lagrangian formulations for differential-difference and fully discrete analogues of the Darboux system. In the continuous and semi-discrete settings, the Lagrangians can be written in terms of elementary functions, specifically logarithms, whereas in the fully discrete case they naturally involve special functions, notably dilogarithms. An additional outcome of this approach is that the dispersionless limits of these Lagrangians yield a complete classification of three-dimensional second-order integrable Lagrangians of certain form.

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com