Multilinear Hirota operators and integrability

TL;DR

This paper introduces a multilinear generalization of the Hirota derivative, demonstrating its role in integrable hierarchies and revealing splittable equations indicative of higher KP reductions.

Contribution

It presents a novel multilinear Hirota operator framework and shows how certain integrable equations can be decomposed into bilinear forms, indicating higher KP reductions.

Findings

Two special multilinear equations are shown to be splittable into bilinear operators.

The splittability signifies higher (B)KP reductions.

The multilinear Hirota derivative serves as a fundamental building block for integrable hierarchies.

Abstract

We consider multilinear generalization of the Hirota derivative, which serves as a building block for integrable solitonic hierarchies. 2 special integrable mutlilinear equations are shown to be splittable into pairs of bilinear operators, parametrized by the additional variable. This fact is a signature of a higher (B)KP reductions.