Integrable (3+1)-dimensional systems with rational Lax pairs

TL;DR

This paper introduces a method to construct new integrable (3+1)-dimensional PDE systems using rational Lax pairs, advancing the understanding of higher-dimensional integrability.

Contribution

It establishes a novel link between rational functions and integrable (3+1)-dimensional systems via contact Lax pairs.

Findings

New class of integrable (3+1)-dimensional systems identified

Rational functions serve as a basis for constructing integrable PDEs

Framework extends the theory of integrability to higher dimensions

Abstract

The search for new integrable (3+1)-dimensional partial differential systems is among the most important challenges in the modern integrability theory. It turns out that such a system can be associated to any pair of rational functions of one variable in general position, as established below using contact Lax pairs introduced in arXiv:1401.2122.