# On deformations of the dispersionless Hirota equation

## TL;DR

This paper explores geometric deformations of the dispersionless Hirota equation via twistor space methods, revealing new structures and connections to hyper-CR Einstein-Weyl geometries.

## Contribution

It introduces a geometric approach to deform the dispersionless Hirota equation, extending recent work and applying to various twistor-related geometric structures.

## Key findings

- Deformations of the Hirota equation are derived from twistor space constructions.
- The method recovers the hyper-CR equation as a special case.
- The approach can be generalized to other geometric structures.

## Abstract

The hyper-CR Einstein-Weyl structures on $\R^3$ can be described in terms of the solutions to the dispersionless Hirota equation. In the present paper we show that simple geometric constructions on the associated twistor space lead to deformations of the Hirota equation that have been introduced recently by B. Kruglikov and A. Panasyuk. Our method produces also the hyper-CR equation and can be applied to other geometric structures related to different twistor constructions.