Higher-Dimensional Integrable Systems from Multilinear Evolution Equations

TL;DR

This paper introduces a multilinear generalization of Lax pairs for higher-dimensional integrable systems, providing explicit forms for a class of time-harmonic hypersurface motions, advancing the understanding of multidimensional integrability.

Contribution

It presents a novel multilinear Lax pair framework for M-dimensional integrable systems, specifically applied to hypersurface motions, expanding the theoretical tools for multidimensional integrability.

Findings

Explicit multilinear Lax pairs for M-dimensional systems

Application to time-harmonic hypersurface motions

Enhanced understanding of higher-dimensional integrable structures

Abstract

A multilinear M-dimensional generalization of Lax pairs is introduced and its explicit form is given for the recently discovered class of time-harmonic, integrable, hypersurface motions.