CKP hierarchy and free Bosons

TL;DR

This paper explores the CKP hierarchy using free Bosons, constructing modified and constrained hierarchies, and analyzing Darboux transformations and symmetries to deepen understanding of integrable properties.

Contribution

It introduces a free Boson framework for the CKP hierarchy, linking Darboux transformations and symmetries to tau functions, and provides new insights into their structure.

Findings

Constructed the modified CKP hierarchy using free Bosons

Derived solutions for the constrained CKP hierarchy

Expressed Darboux transformations and symmetries in terms of free Bosons

Abstract

In this paper, free Bosons are used to study some integrable properties of the CKP hierarchy, from the aspects of tau functions. Firstly, the modified CKP hierarchy is constructed by using free Bosons and the corresponding Lax structure is given. Then the constrained CKP hierarchy is found to be related with the modified CKP hierarchy, and the corresponding solutions are derived by using free Bosons. Next by using the relations between the Darboux transformations and the squared eigenfunction symmetries, we express the Darboux transformations of the CKP hierarchy in terms of free Bosons, by which one can better understand the essential of the CKP Darboux transformations. In particular, the additional symmetries of the CKP hierarchy can be viewed as the infinitesimal generator of the CKP Darboux transformations. Based upon these results, we finally obtain the actions of the CKP additional symmetries on the CKP tau functions constructed by free Bosons.