Abstract
In this paper, free bosons are used to study some integrable properties of Kadomtsev-Petviashvili (KP) hierarchy of C type (CKP hierarchy), from the aspects of tau functions. First, 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 to 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 properties 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 on these results, we finally obtain the actions of the CKP additional symmetries on the CKP tau functions constructed by free bosons.
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