Solutions of the Frobenius coupled KP equation

In this paper, we firstly construct the coupled Schur function solution of the Frobenius coupled Kadomtsev–Petviashvili (KP) hierarchy as a generalization of the Schur function. The Frobenius coupled KP hierarchy contains a Frobenius coupled KP equation which has a potential application in the theory of two-layer shallow water waves. We further derive some regular Wronskian solution and non-Wronskian solutions of the Frobenius coupled KP equation.