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.

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.