Generalized double Casoratian solutions to the four-potential isospectral Ablowitz–Ladik equation

•We study the four-potential isospectral Ablowitz–Ladik equation via a matrix method.•Through the Casoratian technique we get the generalized double Casoratian solutions.•A novel class of explicit solutions are derived by taking special matrices in details.

Generalized solutions in double Casoratian form of the four-potential isospectral Ablowitz–Ladik equation possessing bilinear form are derived through a matrix method for constructing double Casoratian entries. A novel class of explicit solutions, such as soliton, rational-like, Matveev, Complexiton and interaction solutions, are obtained by letting the general matrix be some special cases. Interestingly, a periodic solution is deduced from the Complexiton solution.