A class of reductions of the two-component KP hierarchy and the Hirota-Ohta system

TL;DR

This paper introduces a new class of reductions within the two-component KP hierarchy, including the Hirota-Ohta system, using bilinear identities and Lax operators to characterize these reductions.

Contribution

It provides a novel framework for understanding reductions of the two-component KP hierarchy, connecting bilinear identities with Lax operators and the Hirota-Ohta system.

Findings

Defined a new class of reductions for the two-component KP hierarchy

Characterized reductions using bilinear identities and Lax operators

Included the Hirota-Ohta system within the reduction framework

Abstract

We introduce a class of reductions of the two-component KP hierarchy, which includes the Hirota-Ohta system hierarchy. The description of the reduced hierarchies is based on the Hirota bilinear identity and an extra bilinear relation characterising the reduction. We derive the reduction conditions in terms of the Lax operator and higher linear operators of the hierarchy, as well as in terms of the basic two-component KP system of equations.