ABSTRACT The algebraic structures of integrable hierarchies play an important role in the study of soliton equations. In this paper, we use splitting theory to give a matrix representation of a constrained CKP hierarchy, which can be considered as a generalization of the ‐KdV hierarchy and the constrained KP hierarchy. An equivalent construction in terms of the pseudo‐differential operator is discussed. Darboux transformations, scaling transformations, and tau functions for this constrained hierarchy are studied.
Li et al. (Sun,) studied this question.