# From PDEs to Pfaffian fibrations

## TL;DR

This paper introduces Pfaffian fibrations as an intrinsic way to encode PDEs, generalizing concepts like prolongations and integrability, and providing a new perspective on their geometric structure.

## Contribution

It presents Pfaffian fibrations as a novel, intrinsic framework for understanding PDEs, extending classical geometric notions to a more general setting.

## Key findings

- Pfaffian fibrations encode PDE data intrinsically.
- Prolongations and integrability extend naturally to Pfaffian fibrations.
- Provides a new geometric perspective on PDE analysis.

## Abstract

We explain how to encode the essential data of a PDE on jet bundle into a more intrinsic object called Pfaffian fibration. We provide motivations to study this new notion and show how prolongations, integrability and linearisations of PDEs generalise to this setting.