# Lagrangian multiforms and dispersionless integrable systems

## TL;DR

The paper shows how Lagrangian multiforms naturally arise in multidimensional dispersionless integrable systems through conservation laws and hydrodynamic reductions.

## Contribution

The paper introduces new examples of Lagrangian multiforms in dispersionless integrable systems via conservation laws and hydrodynamic reductions.

## Key findings

- Lagrangian multiforms appear as higher-order conservation laws of linearly degenerate PDEs in 3D.
- They also emerge in the context of Gibbons–Tsarev equations for hydrodynamic reductions of heavenly type equations in 4D.

## Abstract

We demonstrate that interesting examples of Lagrangian multiforms appear naturally in the theory of multidimensional dispersionless integrable systems as (a) higher-order conservation laws of linearly degenerate PDEs in 3D, and (b) in the context of Gibbons–Tsarev equations governing hydrodynamic reductions of heavenly type equations in 4D.