On a matrix constrained CKP hierarchy

2025/10/10 by Li, Song, Tian, Kelei, Wu, Zhiwei
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2510.09054

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 A_2n⁽²⁾-KdV hierarchy and the constrained KP hierarchy. An equivalent construction in terms of the pseudo-differential operator is discussed. Darboux transformations, scaling transformation and tau functions ln τ_f for this constrained hierarchy are studied. Moreover, we present formulas for the Virasoro vector fields on ln τ_f for the A_{2 n}⁽²⁾-KdV hierarchy.

Citations

• Bäcklund transformations for Gelfand-Dickey flows, revisited
• Tau function and Virasoro action for the nxn KdV hierarchy
• Tau functions and Virasoro actions for soliton hierarchies
• The recursion operator for a constrained CKP hierarchy
• On the Inverse Scattering Problem for Cubic Eigenvalue Problems of the Class ψxxx + 6Qψx + 6Rψ = λψ

Related

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• Constrained KP Hierarchies: Darboux-Bäcklund Solutions and Additional Symmetries