Dispersionless (3+1)-dimensional integrable hierarchies

TL;DR

This paper develops a multi-dimensional R-matrix method to construct new (3+1)-dimensional dispersionless integrable hierarchies, expanding the theoretical framework for higher-dimensional integrable systems.

Contribution

It introduces a novel multi-dimensional R-matrix approach applied to contact brackets, leading to new classes of (3+1)-dimensional dispersionless integrable hierarchies.

Findings

Constructed new integrable hierarchies in (3+1) dimensions

Extended the R-matrix method to multi-dimensional settings

Linked the hierarchies to contact bracket structures

Abstract

In the present paper we introduce a multi-dimensional version of the R-matrix approach to the construction of integrable hierarchies. Applying this method to the case of the Lie algebra of functions with respect to the contact bracket, we construct integrable hierarchies of (3+1)-dimensional dispersionless systems of the type recently introduced by one of us in arXiv:1401.2122.