# Nonlocal symmetries, conservation laws, and recursion operators of the Veronese web equation

## TL;DR

This paper investigates the Veronese web equation by constructing nonlocal conservation laws, describing nonlocal symmetries, and developing a recursion operator that reveals new symmetries and master-symmetries.

## Contribution

It introduces a novel recursion operator for the Veronese web equation and characterizes its nonlocal symmetries and conservation laws.

## Key findings

- Two infinite series of nonlocal conservation laws were constructed.
- The Lie algebras of nonlocal symmetries were described in associated differential coverings.
- A new recursion operator acting on nonlocal shadows was developed, revealing a master-symmetry.

## Abstract

We study the Veronese web equation $u_y u_{tx}+ \lambda u_xu_{ty} - (\lambda+1)u_tu_{xy} =0$ and using its isospectral Lax pair construct two infinite series of nonlocal conservation laws. In the infinite differential coverings associated to these series, we describe the Lie algebras of the corresponding nonlocal symmetries. Finally, we construct a recursion operator and explore its action on nonlocal shadows. The operator provides a new shadow which serves as a master-symmetry.