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.