Solutions Construction for the gcmKP Hierarchy via Boson‐Fermion Correspondence

This paper focuses on the generalized constrained modified Kadomtsev–Petviashvili (gcmKP) hierarchy. First, we utilize the boson‐fermion correspondence to transform the Hirota bilinear equations of the gcmKP hierarchy into fermionic form. Based on this representation, we construct explicit rational and soliton solutions by selecting specific group elements in the Lie group , expressing them as vacuum expectation values and presenting concrete examples.