New doubly periodic and multiple soliton solutions of the generalized (3 + 1)-dimensional Kadomtsev–Petviashvilli equation with variable coefficients

A generalized variable-coefficient algebraic method is proposed to construct several new families of exact solutions of physical interest for the (3 + 1)-dimensional Kadomtsev–Petviashvilli (KP) equation with variable coefficients. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with most existing tanh method, the extended tanh method, the Jacobi elliptic function method or the algebraic method, the proposed method gives new and more general solutions.