# Kronecker webs, Nijenhuis operators, and nonlinear PDEs

## TL;DR

This paper surveys Kronecker webs and their connection to bihamiltonian structures and PDEs, and offers a partial solution to bisymplectic realization using partial Nijenhuis operators.

## Contribution

It introduces and studies partial Nijenhuis operators, providing new insights into the realization of bihamiltonian structures and their relation to nonlinear PDEs.

## Key findings

- Survey of Kronecker webs and their relation to PDEs
- Partial solution to bisymplectic realization problem
- Detailed study of partial Nijenhuis operators

## Abstract

The aim of this paper is two-fold. First, a survey of the theory of Kronecker webs and their relations with bihamiltonian structures and PDEs is presented. Second, a partial solution to the problem of bisymplectic realization of a bihamiltonian structure is given. Both the goals are achieved by means of the notion of a partial Nijenhuis operator, which is studied in detail.

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Source: https://tomesphere.com/paper/1705.03522