Solutions for the vector k‐constrained KP hierarchy

A class of (1+1)‐dimensional integrable systems which are constrained from the Kadomtsev–Petviashvili (KP) hierarchy is studied. The bilinear equations of these integrable systems are shown first, and then by using the free fermion operators their rational and soliton solutions which are closely related to the τ functions of the KP hierarchy are obtained. The result implies that a large family of solutions of the (2+1)‐dimensional KP hierarchy can be obtained by solving these (1+1)‐dimensional integrable systems; in particular, the N‐soliton solutions of the KP hierarchy can be deduced from the soliton solutions of these (1+1)‐dimensional integrable systems.