# Matrix extension of the Manakov-Santini system and integrable chiral model on Einstein-Weyl background

## TL;DR

This paper introduces a matrix extension of the Manakov-Santini system, linking it to integrable chiral models on Einstein-Weyl backgrounds, and develops associated hierarchies and dressing schemes.

## Contribution

It presents a novel matrix extension of the Manakov-Santini system and connects it to (2+1)-dimensional integrable chiral models on Einstein-Weyl spaces.

## Key findings

- Developed a dressing scheme for the extended system
- Defined an extended hierarchy of integrable equations
- Connected matrix extensions to Einstein-Weyl geometry

## Abstract

It was demonstrated recently [Dunajski, Ferapontov and Kruglikov (2014)] that the Manakov-Santini system describes a local form of general Lorentzian Einstein-Weyl geometry. We introduce integrable matrix extension of the Manakov-Santini system and show that it describes (2+1)-dimensional integrable chiral model in Einstein-Weyl space. We develop a dressing scheme for the extended MS system and define an extended hierarchy. Matrix extension of Toda type system connected with another local form of Einstein-Weyl geometry is also considered.