Tau functions of the constrained matrix KP hierarchy

2026/07/28 by Xiaohan Fan, Jipeng Cheng, Jinbiao Wang
#nlin.SI

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Abstract

The constrained matrix KP hierarchy (L^k)_<0=∑_i=1^mQ_i∂^-1R_i^\intercal is investigated from the aspects of tau functions. Firstly, the matrix KP hierarchy is viewed as one special reduction of the multi-component KP hierarchy. Then bilinear equations of the constrained matrix KP hierarchy as the multi-component KP hierarchy are given in terms of tau functions. Finally based upon these results, the tau functions for the constrained matrix KP hierarchy are constructed by using the multi-component boson-fermion correspondence. Notice that the solutions of the constrained matrix KP hierarchy are derived without using quasi-determinants.

Citations

• The noncommutative KP hierarchy and its solution via descent algebra
• Multi-component Toda lattice hierarchy
• Multicomponent KP type hierarchies and their reductions, associated to conjugacy classes of Weyl groups of classical Lie algebras
• On a direct approach to quasideterminant solutions of a noncommutative KP equation
• Quasideterminants

Related

• On matrix modified KP hierarchy
• Polynomial tau-functions for the multi-component KP hierarchy
• Multi-Component Matrix KP Hierarchies as Symmetry-Enhanced Scalar KP Hierarchies and Their Darboux-B"acklund Solutions
• Tau-function of the multi-component CKP hierarchy
• The constrained KP hierarchy and the bigraded Toda hierarchy of (M,1)-type