WDVV Equations, Darboux-Egoroff Metric and the Dressing Method

TL;DR

This paper uses dressing techniques to construct integrable structures behind WDVV equations, linking commuting flows to isomonodromic flows, with explicit examples in low dimensions including Landau-Ginzburg models.

Contribution

It introduces a dressing method to build integrable structures for WDVV equations and provides explicit low-dimensional examples, including Landau-Ginzburg potentials.

Findings

Constructed commuting Lax operators for WDVV equations.

Linked commuting flows to isomonodromic flows.

Provided explicit 2D and 3D examples, including Landau-Ginzburg models.

Abstract

Dressing technique is used to construct commuting Lax operators which provide an integrable (canonical) structure behind Witten--Dijkgraaf--Verlinde--Verlinde equations. The commuting flows are related to the isomonodromic flows. Examples of the canonical integrable structure are given in two- and three-dimensional cases. The three-dimensional example is associated with the rational Landau-Ginzburg potentials.